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# Counting

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29
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In how many ways can you spell the word FOOT in the grid below?  You can start on any letter F, then on each step you can step one letter in any direction (up, down, left, right, or diagonal)

\begin{array}{cccc} F & F & F & F \\ T & O & O & T \\ T & O & O & T \\ F & F & F & F \end{array}

Nov 13, 2021

#1
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We can solve this pretty easily by using casework.

Case 1: Starting with F in the middle

If we start with F in the middle, there are 4 choices for F. Then we have 2 choices for O, 3 choices for the second O, and 2 choices for the T.

Case 2: Starting with F in the corner

If we start with F in the corner, there are 4 choices for F. Then we have 1 choice for O, 3 choices for the second O, and 2 choices for T.

Adding these up, we have 24 + 48 = 72 ways to spell FOOT.

Nov 13, 2021