You’re probably familiar with the game of Scrabble. The tiles in themselves have values between 1 and 10, but there are also premium squares that increase the scoring value of a tile when it is played. For example, the letter H normally scores 4, but if placed on a double letter square, its value increases to 8. If this same H on a double letter square is part of a word for which a triple word score is awarded, then the value triples again to 24. If the same tile is used to make two words at the same time, its scoring value is the sum of two values, one for each word.
On this basis, what is the highest possible scoring value that a single tile can have on the turn in which it is played?
Fill the grid with the numbers from 1 to 9, such that each number appears exactly once in each row, each column and each of the nine 3×3 blocks.
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Move three matches to make nine squares.
Starting with the same pattern, move eight matches to make fifteen squares.