Problem 19 · 2015 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracingcasework
For the game of chess a new piece, the Kangaroo, has been invented. With each jump the kangaroo jumps either 3 squares vertically and 1 horizontally, or 3 horizontally and 1 vertically, as pictured. What is the smallest number of jumps the kangaroo must make to move from its current position to position A?
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Answer: B — 3
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Hint 1 of 2
Square A is only a short step away, but every jump is long (3 one way, 1 the other), so you must overshoot and come back.
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Hint 2 of 2
Check that one or two jumps can never land exactly on A, then find a route that works.
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Approach: rule out the short jump counts, then exhibit a 3-jump path
- Square A sits just one square diagonally from the start, while each jump moves a total of 4 squares (3 + 1), so a single jump lands far away.
- Two jumps can be checked to never end exactly on A's square.
- Three well-chosen jumps (overshooting and stepping back) do land on A, so the smallest number of jumps is 3.
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