Lovers meet - Part 6

Probability Level 2

Anna and Ben live at opposite corners of a 3 by 3 block.
If Anna only moves right or up or down, and isn't allowed to retrace her steps, how many ways does she have to get to Ben?

12 9 8 6

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Noor MAlik
Jul 5, 2015

It can be proved that for a figure with number of "squares" even, the number of ways Anna can reach Ben is simply the product of the dimensions. In this case, the answer is 3 ∗ 3 = 9 \displaystyle 3*3 = \boxed{9}

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No, that claim is not true. In a 2 by 2 grid, there are 2 ways, and not 2 × 2 = 4 2 \times 2 = 4 . See the previous problem.

Chung Kevin - 5 years, 11 months ago

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No i said the squares formed on the picture, not the dimensions of the block, in this question the dimensions are 3x3 but there are 4 "blocks". THat's what I mean by a square. And I"m pretty sure this claim is true.

Noor MAlik - 5 years, 11 months ago

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See the general case . When it's a 5 by 5 grid, (or 4 by 4 "squares"), the answer is 5 4 5^ 4 , and not 5 × 5 5 \times 5 .

You claim is only true in this very particular case.

Chung Kevin - 5 years, 11 months ago

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