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).![\[\begin{array}{ccccc} R&R&R&R&R\\ M&O&O&O&M\\ M&O&O&O&M\\ M&O&O&O&M\\ R&R&R&R&R \end{array}\]](/api/ssl-img-proxy?src=https%3A%2F%2Flatex.artofproblemsolving.com%2F3%2F9%2F4%2F3947544aa6373e4acb21292480b96c874a92bf5e.png)
I tried looking at the other answer, but it didn't make much sense. First things first, I noticed that (I'm pretty sure) you can't use the center o in any of the cases. But from there, I'm stuck.
There are 4 that have 1 entry point from the C, and you can't use the middle C, because if you get there, there is nothing to go to: 4(1*1*3) makes 12 (you have to move diagonally away, then vertical, then you are at the middle and can go diagonally or horizontal, making 3 possibilities.)
Starting from the middle outside: 4(2 + 10 = 12) = 48.
Staring from the top and bottom center: 2(2 + 3 + 3 + 2 = 10) = 20.
So there are 48 + 20 = 68 ways.
+118609 I saw this question just a moment ago.
How many times to you need to ask the same question?
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