Is this a trick?????
Geometry
Level
pending
A 5x5 grid is divided into 25 small 1x1 squares. Each small square has a frog inside. After a whistle, each frog jumps into an adjacent square. What is the least possible number of squares with at least 2 frogs in it?
0
3
1
2
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1 solution
Color the grid alternatively with black and white, with the top left corner square black. There are 13 black and 12 white squares. After the whistle, each frog in a black square (there are 13 of them) is now in a white square. So one white square must have at least two frogs in it. It is easy to construct a way of jumping resulting in only one such square: just pick a path through all the squares once, and make the frogs jump to the next one in the path, with the last one jumps to any adjacent square.