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Line element

2025-07-16T21:45:07Z

2A00:23C5:FE1C:3701:FDB3:C44F:4F50:7012: format

{{Short description|Line segment of infinitesimally small length}}
{{about|lines in mathematics|Long Interspersed Nuclear Elements in DNA|Retrotransposon#LINEs}}

In [[geometry]], the '''line element''' or '''length element''' can be informally thought of as a line segment associated with an [[infinitesimal]] [[displacement vector]] in a [[metric space]]. The length of the line element, which may be thought of as a differential [[arc length]], is a function of the [[metric tensor]] and is denoted by ''<math>ds</math>''.

Line elements are used in [[physics]], especially in theories of [[gravitation]] (most notably [[general relativity]]) where [[spacetime]] is modelled as a curved [[pseudo-Riemannian manifold]] with an appropriate [[metric tensor (general relativity)|metric tensor]].<ref name="WheelerMisnerThorne">Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, {{isbn|0-7167-0344-0}}</ref>

==General formulation==

{{for|notation used|Ricci calculus|Einstein notation}}

===Definition of the line element and arc length===

The [[coordinate]]-independent definition of the square of the line element ''ds'' in an ''n''-[[dimension]]al [[Riemannian manifold|Riemannian]] or [[pseudo-Riemannian manifold]] (in physics usually a [[spacetime manifold|Lorentzian manifold]]) is the "square of the length" of an infinitesimal displacement <math>d\mathbf{q}</math><ref name="Kay">Tensor Calculus, D.C. Kay, Schaum’s Outlines, McGraw Hill (USA), 1988, {{isbn|0-07-033484-6}}</ref> (in pseudo-Riemannian manifolds possibly negative) whose square root should be used for computing curve length:
<math display="block"> ds^2 = d\mathbf{q}\cdot d\mathbf{q} = g(d\mathbf{q},d\mathbf{q})</math>
where ''g'' is the [[metric tensor]], '''·''' denotes [[inner product]], and ''d'''''q''' an [[infinitesimal]] [[Displacement (vector)|displacement]] on the (pseudo) Riemannian manifold. By parametrizing a curve <math>\mathbf{q}(\lambda)</math>, we can define the [[arc length]] of the curve length of the curve between <math>\mathbf{q}_1=\mathbf{q}(\lambda_1)</math>, and <math>\mathbf{q}_2=\mathbf{q}(\lambda_2)</math> as the [[integral]]:<ref name="SpiegelLipschutzSpellman">Vector Analysis (2nd Edition), M.R. Spiegel, S. Lipcshutz, D. Spellman, Schaum’s Outlines, McGraw Hill (USA), 2009, {{isbn|978-0-07-161545-7}}</ref>
<math display="block"> s = \int_{\mathbf{q}_1}^{\mathbf{q}_2}\sqrt{ \left|ds^2\right|} = \int_{\lambda_1}^{\lambda_2} d\lambda \sqrt{ \left|g\left(\frac{d\mathbf{q}}{d\lambda},\frac{d\mathbf{q}}{d\lambda}\right)\right|} = \int_{\lambda_1}^{\lambda_2} d\lambda \sqrt{ \left|g_{ij}\frac{dq^i}{d\lambda}\frac{dq^j}{d\lambda}\right|}.</math>

To compute a sensible length of curves in pseudo Riemannian manifolds, it is best to assume that the infinitesimal displacements have the same sign everywhere. E.g. in physics the square of a line element along a timeline curve would (in the <math>-+++</math> signature convention) be negative and the negative square root of the square of the line element along the curve would measure the proper time passing for an observer moving along the curve.
From this point of view, the metric also defines in addition to line element the [[surface (topology)|surface]] and [[volume element]]s etc.

===Identification of the square of the line element with the metric tensor===
Since <math>d\mathbf{q}</math> is an arbitrary "square of the arc length", <math>ds^2</math> completely defines the metric, and it is therefore usually best to consider the expression for <math>ds^2</math> as a definition of the metric tensor itself, written in a suggestive but non tensorial notation:
<math display="block">ds^2 = g</math>
This identification of the square of arc length <math>ds^2</math> with the metric is even more easy to see in ''n''-dimensional general [[curvilinear coordinates]] {{nowrap|1='''q''' = (''q''1, ''q''2, ''q''3, ..., ''qn'')}}, where it is written as a symmetric rank 2 tensor<ref name="SpiegelLipschutzSpellman"/><ref>An introduction to Tensor Analysis: For Engineers and Applied Scientists, J.R. Tyldesley, Longman, 1975, {{isbn|0-582-44355-5}}</ref> coinciding with the metric tensor:
<math display="block"> ds^2= g_{ij} dq^i dq^j = g .</math>

Here the [[Ricci calculus|indices]] ''i'' and ''j'' take values 1, 2, 3, ..., ''n'' and [[Einstein summation convention]] is used. Common examples of (pseudo-) Riemannian spaces include [[three-dimensional]] [[space]] (no inclusion of [[time]] coordinates), and indeed [[four-dimensional]] [[spacetime]].

==Line elements in Euclidean space==
{{main|Euclidean space}}

[[File:Line element.svg|thumb|Vector line element d'''r''' (green) in [[three-dimensional|3d]] Euclidean space, where λ is a [[parametric equation|parameter]] of the space curve (light green).]]

Following are examples of how the line elements are found from the metric.

===Cartesian coordinates===

The simplest line element is in [[Cartesian coordinates]] - in which case the metric is just the [[Kronecker delta]]:
<math display="block">g_{ij} = \delta_{ij}</math>
(here ''i, j'' = 1, 2, 3 for space) or in [[matrix (mathematics)|matrix]] form (''i'' denotes row, ''j'' denotes column):
<math display="block">[g_{ij}] = \begin{pmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix}</math>

The general curvilinear coordinates reduce to Cartesian coordinates:
<math display="block">(q^1,q^2,q^3) = (x, y, z)\,\Rightarrow\,d\mathbf{r}=(dx,dy,dz)</math>
so
<math display="block"> ds^2 = g_{ij} dq^i dq^j = dx^2 +dy^2 +dz^2 </math>

===Orthogonal curvilinear coordinates===

For all [[orthogonal coordinates]] the metric is given by:<ref name="SpiegelLipschutzSpellman"/>
<math display="block">[g_{ij}] = \begin{pmatrix}
h_1^2 & 0 & 0\\
0 & h_2^2 & 0\\
0 & 0 & h_3^2
\end{pmatrix}</math>
where
<math display="block">h_i = \left|\frac{\partial\mathbf{r}}{\partial q^i}\right|</math>

for ''i'' = 1, 2, 3 are [[curvilinear coordinates#Orthogonal curvilinear coordinates in 3d|scale factor]]s, so the square of the line element is:
<math display="block">ds^2 = h_1^2(dq^1)^2 + h_2^2(dq^2)^2 + h_3^2(dq^3)^2 </math>

Some examples of line elements in these coordinates are below.<ref name="Kay"/>

{| class="wikitable"
|-
! Coordinate system
! {{math|(''q''1, ''q''2, ''q''3)}}
! Metric
! Line element
|-
|[[Cartesian coordinate system|Cartesian]]
|{{math|(''x'', ''y'', ''z'')}}
|<math>[g_{ij}] = \begin{pmatrix}
1 & 0 & 0\\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{pmatrix}</math>
|<math> ds^2 = dx^2 + dy^2 + dz^2 </math>
|-
|[[Polar coordinate system|Plane polars]]
|{{math|(''r'', ''θ'')}}
|<math>[g_{ij}] = \begin{pmatrix}
1 & 0 \\
0 & r^2 \\
\end{pmatrix}</math>
|<math> ds^2= dr^2 +r^2 d \theta^2</math>
|-
|[[Spherical coordinate system|Spherical polar]]s
|{{math|(''r'', ''θ'', ''φ'')}}
|<math>[g_{ij}] = \begin{pmatrix}
1 & 0 & 0 \\
0 & r^2 & 0 \\
0 & 0 & r^2\sin^2\theta \\
\end{pmatrix}</math>
|<math> ds^2=dr^2+r^2 d \theta\ ^2+ r^2 \sin^2 \theta d \varphi^2 </math>
|-
|[[Cylindrical polar coordinates|Cylindrical polar]]s
|{{math|(''r'', ''φ'', ''z'')}}
|<math>[g_{ij}] = \begin{pmatrix}
1 & 0 & 0 \\
0 & r^2 & 0 \\
0 & 0 & 1 \\
\end{pmatrix}</math>
|<math> ds^2=dr^2+ r^2 d \varphi^2 +dz^2 </math>
|}

==General curvilinear coordinates==

Given an arbitrary basis <math>\{\hat{b}_{i}\}</math> of a space of dimension <math> n </math>, the metric is defined as the inner product of the basis vectors.
<math display="block">g_{ij}=\langle\hat{b}_{i},\hat{b}_{j}\rangle</math>

Where <math>1\leq i,j\leq n</math> and the inner product is with respect to the ambient space (usually its <math>\delta_{ij}</math>)

In a coordinate basis <math>\hat{b}_{i} = \frac{\partial}{\partial x^{i}}</math>

The coordinate basis is a special type of basis that is regularly used in differential geometry.

==Line elements in 4d spacetime==

===Minkowski spacetime===

The [[Minkowski metric]] is:<ref>Relativity DeMystified, D. McMahon, Mc Graw Hill (USA), 2006, {{isbn|0-07-145545-0}}</ref><ref name="WheelerMisnerThorne"/>
<math display="block">[g_{ij}] = \pm \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 \\
\end{pmatrix}</math>
where one sign or the other is chosen, both conventions are used. This applies only for [[flat spacetime]]. The coordinates are given by the [[4-position]]:
<math display="block">\mathbf{x} = (x^0,x^1,x^2,x^3) = (ct,\mathbf{r}) \,\Rightarrow\, d\mathbf{x} = (c dt, d\mathbf{r})</math>

so the line element is:
<math display="block">ds^2 = \pm (c^2 dt^2 - d\mathbf{r} \cdot d\mathbf{r}) .</math>

===Schwarzschild coordinates===

In [[Schwarzschild coordinates]] coordinates are <math> \left(t, r, \theta, \phi \right)</math>, being the general metric of the form:
<math display="block">[g_{ij}] = \begin{pmatrix}
-a(r)^2 & 0 & 0 & 0 \\
0 & b(r)^2 & 0 & 0 \\
0 & 0 & r^2 & 0 \\
0 & 0 & 0 & r^2 \sin^2\theta \\
\end{pmatrix}</math>

(note the similitudes with the metric in 3D spherical polar coordinates).

so the line element is:
<math display="block">ds^2 = -a(r)^2 \, dt^2 + b(r)^2 \, dr^2 + r^2 \, d\theta^2 + r^2 \sin^2\theta \, d\phi^2 .</math>

===General spacetime===

The coordinate-independent definition of the square of the line element d''s'' in [[Spacetime#Spacetime intervals|spacetime]] is:<ref name="WheelerMisnerThorne"/>
<math display="block"> ds^2 = d\mathbf{x} \cdot d\mathbf{x} = g(d\mathbf{x},d\mathbf{x}) </math>

In terms of coordinates:
<math display="block"> ds^2 = g_{\alpha\beta} dx^\alpha dx^\beta </math>
where for this case the indices {{math|''α''}} and {{math|''β''}} run over 0, 1, 2, 3 for spacetime.

This is the [[spacetime interval]] - the measure of separation between two arbitrarily close [[Event (relativity)|events]] in [[spacetime]]. In [[special relativity]] it is invariant under [[Lorentz transformation]]s. In [[general relativity]] it is invariant under arbitrary [[inverse function|invertible]] [[Differentiable function|differentiable]] [[coordinate transformations]].

==See also==

*[[Covariance and contravariance of vectors]]
*[[First fundamental form]]
*[[List of integration and measure theory topics]]
*[[Metric tensor]]
*[[Ricci calculus]]
*[[Raising and lowering indices]]
*[[Volume element]]

==References==

{{reflist}}

[[Category:Affine geometry]]
[[Category:Riemannian geometry]]
[[Category:Special relativity]]
[[Category:General relativity]]

[[da:Linjeelement]]
[[de:Linienelement]]

Super Scrabble

2025-07-16T16:46:59Z

2A00:23C5:FE1C:3701:FDB3:C44F:4F50:7012: hyphen reqd

{{Short description|Board game based on Scrabble}}
{{refimprove|date=September 2018}}
[[File:Super Scrabble (1187786082).jpg|thumb|A ''Super Scrabble'' game]]
'''''Super Scrabble''''' is a [[board game]] introduced in 2004 and a variant of ''[[Scrabble]]''. It is played on a 21×21 grid board instead of Scrabble's usual 15×15, and uses twice as many letter tiles.

In North America ''Super Scrabble'' is made and marketed by Winning Moves Games, but licensed by [[Hasbro]]. In the rest of the world it is manufactured by Tinderbox Games under license from [[Mattel]]. ''Super Scrabble'' is available in [[English language|English]] and German. In February 2007, a ''Deluxe Super Scrabble'' was released with a rotating gameboard and interlocking tiles, just like ''Deluxe Scrabble''.

==Gameplay differences==
The changes from standard ''Scrabble'' in ''Super Scrabble'' are summarized by the latter's tagline, "More spaces, more tiles, more points—add to your fun!" The board is larger (21×21 or 441 squares vs. 15×15 or 225 squares); there are more premium squares (going up to quadruple letter and word score spaces); there are 200 tiles, twice as many as a normal ''Scrabble'' set. The middle 15×15 squares are identical to a ''Scrabble'' board, so standard ''Scrabble'' may be played on a ''Super Scrabble'' board. All the high-scoring quadruple premiums lie near the outside of the board, with the quadruple word squares at the four corners of the board.

Other than the differences in the board and the number of tiles, gameplay is similar to ''Scrabble''. Each player has seven tiles in their rack as normal, scoring is the same, and the same word lists are used. However, the differences are enough to upset normal ''Scrabble'' strategies. For example, earning fifty points in a bingo bonus (using all seven tiles) is not nearly as significant when compared to the high final scores. For a two-player game, scores over eight hundred points are not uncommon.

Tournament-level ''Scrabble'' games are usually limited to two players. Many tournament players find games with more players cramped. With its larger board, ''Super Scrabble'' is ideally suited for three- and four-player games. Indeed, its scoring sheets do not have enough lines to keep score for most two-player games.

''Super Scrabble'' has exactly twice as many tiles as ''Scrabble'', but the distribution of letters is not simply the [[Scrabble letter distributions|original distribution]] doubled. The distribution is:

*4 blank tiles (scoring 0 points)
*''1 point'': '''E''' ×24, '''A''' ×16{{down}}, '''O''' ×15{{down}}, '''T''' ×15{{up}}, '''I''' ×13{{down}}, '''N''' ×13{{up}}, '''R''' ×13{{up}}, '''S''' ×10{{up}}, '''L''' ×7{{down}}, '''U''' ×7{{down}}
*''2 points'': '''D''' ×8, '''G''' ×5{{down}}
*''3 points'': '''C''' ×6{{up}}, '''M''' ×6{{up}}, '''B''' ×4, '''P''' ×4
*''4 points'': '''H''' ×5{{up}}, '''F''' ×4, '''W''' ×4, '''Y''' ×4, '''V''' ×3{{down}}
*''5 points'': '''K''' ×2
*''8 points'': '''J''' ×2, '''X''' ×2
*''10 points'': '''Q''' ×2, '''Z''' ×2

The {{up}} and {{down}} indicate modifications from double the original distribution, with {{up}} indicating more than double the original distribution, and {{down}} indicating fewer. Note, for example, that there are more than twice as many S's (ten, whereas standard ''Scrabble'' has four). This was done to make more opportunities for plurals and third-person singular verbs.

Due to the board and letter distribution alterations, the highest theoretical score from one word is 11520, scored from the word BENZALPHENYLHYDRAZONE (using the two Z tiles and a x144 multiplier from the TWSs and QWSs). How the word on the board can be constructed is currently unknown.

{| class="floatright" style="font-weight: bold; text-align: center; border-collapse: collapse; height: 50%; font-size: 80%; vertical-align: center;"
|-
| style="width: 1.5em;" |
| style="width: 1.5em;" | A
| style="width: 1.5em;" | B
| style="width: 1.5em;" | C
| style="width: 1.5em;" | D
| style="width: 1.5em;" | E
| style="width: 1.5em;" | F
| style="width: 1.5em;" | G
| style="width: 1.5em;" | H
| style="width: 1.5em;" | I
| style="width: 1.5em;" | J
| style="width: 1.5em;" | K
| style="width: 1.5em;" | L
| style="width: 1.5em;" | M
| style="width: 1.5em;" | N
| style="width: 1.5em;" | O
| style="width: 1.5em;" | P
| style="width: 1.5em;" | Q
| style="width: 1.5em;" | R
| style="width: 1.5em;" | S
| style="width: 1.5em;" | T
| style="width: 1.5em;" | U
| style="width: 1.5em;" |
|-
| style="width: 1.5em;" | 1
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: maroon;" | 4× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: maroon;" | 4× WS
| style="width: 1.5em;" | 1
|-
| style="width: 1.5em;" | 2
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 2
|-
| style="width: 1.5em;" | 3
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 3
|-
| style="width: 1.5em;" | 4
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em;" | 4
|-
| style="width: 1.5em;" | 5
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 5
|-
| style="width: 1.5em;" | 6
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 6
|-
| style="width: 1.5em;" | 7
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 7
|-
| style="width: 1.5em;" | 8
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em;" | 8
|-
| style="width: 1.5em;" | 9
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 9
|-
| style="width: 1.5em;" | 10
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 10
|-
| style="width: 1.5em;" | 11
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; color: black; background-color: pink;" | [[File:Five Pointed Star Solid.svg|15px]]
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em;" | 11
|-
| style="width: 1.5em;" | 12
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 12
|-
| style="width: 1.5em;" | 13
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 13
|-
| style="width: 1.5em;" | 14
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em;" | 14
|-
| style="width: 1.5em;" | 15
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 15
|-
| style="width: 1.5em;" | 16
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 16
|-
| style="width: 1.5em;" | 17
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 17
|-
| style="width: 1.5em;" | 18
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black;" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em;" | 18
|-
| style="width: 1.5em;" | 19
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: navy;" | 4× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 19
|-
| style="width: 1.5em;" | 20
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: royalblue;" | 3× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: pink;" | 2× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em;" | 20
|-
| style="width: 1.5em;" | 21
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: maroon;" | 4× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: firebrick;" | 3× WS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: black; background-color: skyblue;" | 2× LS
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; background-color: rgba(128, 128, 128, 0.25);" |
| style="width: 1.5em; border: 1px solid black; line-height: 80%; font-size: 70%; color: white; background-color: maroon;" | 4× WS
| style="width: 1.5em;" | 21
|-
| style="width: 1.5em;" |
| style="width: 1.5em;" | A
| style="width: 1.5em;" | B
| style="width: 1.5em;" | C
| style="width: 1.5em;" | D
| style="width: 1.5em;" | E
| style="width: 1.5em;" | F
| style="width: 1.5em;" | G
| style="width: 1.5em;" | H
| style="width: 1.5em;" | I
| style="width: 1.5em;" | J
| style="width: 1.5em;" | K
| style="width: 1.5em;" | L
| style="width: 1.5em;" | M
| style="width: 1.5em;" | N
| style="width: 1.5em;" | O
| style="width: 1.5em;" | P
| style="width: 1.5em;" | Q
| style="width: 1.5em;" | R
| style="width: 1.5em;" | S
| style="width: 1.5em;" | T
| style="width: 1.5em;" | U
| style="width: 1.5em;" |
|-
|
| colspan=10 style="font-weight: normal; text-align: left;" | {{legend|maroon|Quadruple word score}}
{{legend|firebrick|Triple word score}}
{{legend|pink|Double word score}}
|
| colspan=10 style="font-weight: normal; text-align: left;" | {{legend|navy|Quadruple letter score}}
{{legend|royalblue|Triple letter score}}
{{legend|skyblue|Double letter score}}
|
|-
| colspan=23 style="font-weight: normal; text-align: left;" | The board design used in Super Scrabble.
|}

==Strategy==
Many of the same strategies that are applied in standard ''Scrabble'' play can be utilized in this version. Premiums play a larger role in ''Super Scrabble'', due to both the presence of quadruple letter and word scores, and also because near the edge of the board, double word scores are spaced closely together, making it much easier to score a "double-double". In addition, opportunities for bingos are increased due to the three extra squares in each direction. For the same reason, hooks can play a larger part in strategy (a hook is a letter that can be played at the start or end of a word already on the board and as part of the same move in a new word in the cross direction).

Certain high-scoring words that are impossible to make in ''Scrabble'' without using blanks, such as words with doubled Z's (e.g. FUZZ, JAZZ, DAZZLE), and words with doubled K's (e.g. KICK, KINK, KNOCK, KARAOKE), can be played. The word KNICKKNACK, with 4 K's, cannot be played in ''Scrabble'' because there is only 1 K and only 2 blanks - but it is possible to play this word in ''Super Scrabble''. The same is true for words with four Z's, such as PIZZAZZ and RAZZMATAZZ. With quadruple-letter scores spaced only three squares away from a double-word score, it is not uncommon to see a single play score over one hundred points, even without a fifty-point bonus. Guarding against such plays becomes vital to strategy. However, due to the larger size of the board, this becomes increasingly difficult, especially late in the game.

==External links==
*{{bgg|11182}}, including [http://www.boardgamegeek.com/image/52794 A ''Super Scrabble'' board]
* [https://web.archive.org/web/20080610095038/http://www.winning-moves.com/B248E7C47573406FA00E4443EFE8E0F7.asp?p_key=7F431D46D3AD4FE9BE0B6DF0A5A3308B&type=auto_single&path=Home+%3E+Family%2FAdult+Games&spath=&cat_id=CEA0647E154D4470B2EDAE82CC9948C9&pc_key=D45D58BEB2004F3C9BF44C142D689F54&pcs_key= ''Super Scrabble'' page], Link to ''Deluxe Super Scrabble'' page on Winning Moves USA's website
* [http://www.winning-moves.com/974AC834972648769F406DE95E835622.asp?ccb_key=CB35B64548014684B81A837E7C50A12B Rules], Link to the game's rules on the Winning Moves USA site

{{Scrabble}}

[[Category:Board games introduced in 2004]]
[[Category:Scrabble variants]]
[[Category:Winning Moves games]]