Difference between revisions of "2014 UMO Problems/Problem 6"
(Created page with "==Problem == Draw <math>n</math> rows of <math>2n</math> equilateral triangles each, stacked on top of each other in a diamond shape, as shown below when <math>n = 3</math>. Set...") |
m (→See Also) |
||
Line 37: | Line 37: | ||
== See Also == | == See Also == | ||
{{UMO box|year=2014|num-b=5|after=Last Problem}} | {{UMO box|year=2014|num-b=5|after=Last Problem}} | ||
+ | |||
+ | [[Category:Intermediate Combinatorics Problems]] |
Revision as of 15:31, 14 October 2014
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 |