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enya is standing in the centre square of a 9 by 9 grid. she travels outward one square at a time, moving diagonally or along a row of column. how many difrent paths can enya follow to the perimter?
Hello student,Please find the answer to your question belowshe has 320 unique paths to a perimeter square.Standing on the center square, she has 8 possible squares she can move to to be in what one might call Ring 1 (relative to the single center square).Those 8 squares are not identical in the number of Ring 2 squares they touch. The corner squares each touch 5 Ring 2 squares for a total of 20 unique paths. The squares between the corners (4 squares in this ring) each touch 3 Ring 2 squares for a total of 12 more unique paths: 20 + 12 = 32. So 40 so far.The same thing happens in each ring as one moves outward. 4 corner squares with 5 choices, and however many (3, 5) in between with 3 choices each. They total 320.
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