In how many ways can you spell the word ROOM in the grid below? You can start on any letter R, then on each step you can step on
e letter in any direction (up, down, left, right, or diagonal).
2 answers:
Answer:
96
Step-by-step explanation:
In a straight line, the word can only be spelled on the diagonals, and there are only two diagonals in each direction that have 2 O's.
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If 90° and reflex turns are allowed, then the number substantially increases.
Corner R: can only go to the adjacent diagonal O, and from there to one other O, then to any of the 3 M's, for a total of 3 paths.
2nd R from the left: can go to either of two O's, one of which is the same corner O as above. So it has the same 3 paths. The center O can go to any of 4 Os that are adjacent to an M, for a total of 10 more paths. That's 13 paths from the 2nd R.
Middle R can go the three O's on the adjacent row, so can access the three paths available from each corner O along with the 10 paths available from the center O, for a total of 16 paths.
Then paths accessible from the top row of R's are 3 +13 +16 +13 +3 = 48 paths. There are two such rows of R's so a total of 96 paths.
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