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 one letter in any direction (up, down, left, right, or diagonal).

  84? Not sure but pretty sure

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.

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 +10 +16 +10 +3 = 42 paths. There are two such rows of R's so a total of 84 paths.