Problem 29 · 2014 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracing
On a pond, 16 lily pads are arranged in a \(4\times 4\) grid as shown in the diagram. A frog sits on a lily pad in one of the corners of the grid (see picture). The frog jumps from one lily pad to another horizontally or vertically, always jumping over at least one lily pad, and never lands on the same lily pad twice. What is the maximum number of lily pads, including the one he starts on, on which he can land?
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Answer: A — 16
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Hint 1 of 2
Each jump skips at least one pad, so from a column or row the frog lands two or more cells away.
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Hint 2 of 2
Try to build a route that visits every pad without repeating; can all 16 be reached?
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Approach: construct a route touching every pad
- From a corner the frog can hop horizontally or vertically, always clearing at least one pad in between.
- Designing the path carefully, it is possible to thread through every row and column so that no pad is repeated.
- Such a route reaches all of them, so the maximum number of pads is the full 16.
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