Difference between revisions of "2014 UMO Problems/Problem 6"
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draw((12.5+sqrt(3)/2,sqrt(3)-1/2)--(12.5,sqrt(3)+1),arrow=Arrow()); | draw((12.5+sqrt(3)/2,sqrt(3)-1/2)--(12.5,sqrt(3)+1),arrow=Arrow()); | ||
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== Solution == | == Solution == |
Revision as of 15:20, 12 February 2020
Problem
Draw rows of equilateral triangles each, stacked on top of each other in a diamond shape, as shown below when . Set point as the southwest corner and point as the northeast corner. A step consists of moving from one point to an adjacent point along a drawn line segment, in one of the four legal directions indicated. A path is a series of steps, starting at and ending at , such that no line segment is used twice. One path is drawn below. Prove that for every positive integer , the number of distinct paths is a perfect square. (Note: A perfect square is a number of the form , where is an integer).
Solution
See Also
2014 UMO (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All UMO Problems and Solutions |