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You are given a Chess board with black and white squares.

  • You must fill your Chess board with Merriam Webster English words, or other equivalent dictionnaries if you prefer such that each square contains a letter ;

  • You can fill vertically or horizontally but not diagonaly ;

  • You can have more than one word in a row or column. For instance: puzzle and be ;

  • You can only use a word once.

On your final grid, a letter (actually several is also mathematically possible) will be more frequent than all the other letters. Your aim is that this letter appears as much as possible. If it appears on a white square, you score one and if it appears on a black square, you will score two.

On the next incomplete example, letter E is the most frequent, it appears 6 times. Twice in a black square and four times in a white one. So, up to now, this example scores 8. It is not complete because 25 squares are empty on bottom right and 10 are also missing on bottom left.

enter image description here

Note that the different words used on this example are:

Examples, A, Puzzles, Puzzle, Be and Chess.

Which grid with highest score can you find?

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2 Answers 2

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The rules of the question state that:

On your final grid, a letter (actually several is also mathematically possible) will be more frequent than all the other letters. Your aim is that this letter appears as much as possible.

If we interpret this to mean that all letters appearing with the greatest frequency contribute to the score then it is possible to achieve:

the maximum score of 96!

Like so:

enter image description here

Here, the letters A, E, S and T appear with equal (and greatest) frequency - 16 times each. Under this interpretation of the rules, every space scores points! With 2 for a black and 1 for a white, that makes 64 + 32 = 96 points total.

The words in the diagram above are:

SEATS / TEA
SEAT / TEAS
SATES / EAT
SATE / EATS
TEATS / SEA
TEAT / SEAS
SAT / TEASE
AT / TEASES

All are common dictionary words.

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    $\begingroup$ Best abuse of the rules 2020 $\endgroup$
    – Bubbler
    Oct 29, 2020 at 23:49
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    $\begingroup$ @chasly Note that the OP's own example included both PUZZLE and PUZZLES - it doesn't matter if words appear multiple times within other words, you just have to use different words. All 16 of the words I have made the decision to use (listed in my answer) are unique and thus valid! :) $\endgroup$
    – Stiv
    Oct 30, 2020 at 13:11
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    $\begingroup$ @KingLogic Pretty sure - 2 for a black, 1 for a white, 32 of each, all used :) $\endgroup$
    – Stiv
    Oct 30, 2020 at 17:44
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    $\begingroup$ @KingLogic Those changes would make the e appear more frequently than the other letters, so he would lose a ton of points. This only works because each letter appears the same number of times, so every single square is pointed. Since he gets points for every square, he has the absolute maximum number of points $\endgroup$
    – Anthony Ingram-Westover
    Oct 30, 2020 at 18:41
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    $\begingroup$ I am only disappointed that 'tsetse' is not one of the words used. $\endgroup$
    – fluffysheap
    Oct 30, 2020 at 22:12
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To start things off, here's one with a score of 70

enter image description here

The words are

eleven
ex
tehee
eve
exede
see
levee
ewe
eke
pewee
resee
ere
ebenezer
melee
eye

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    $\begingroup$ All black squares with an "e". That is sort of beautiful :) $\endgroup$
    – JKHA
    Oct 29, 2020 at 23:06
  • $\begingroup$ The other two high-efficiency words you could try and squeeze in are "ere" and "epee", which could potentially get you up to 72. $\endgroup$
    – Misha Lavrov
    Oct 30, 2020 at 20:35
  • $\begingroup$ Definitely +1 and deserves to be co-ticked if possible :) $\endgroup$
    – JKHA
    Nov 6, 2020 at 13:30

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