Difference between revisions of "2013 UMO Problems/Problem 1"
(Created page with "== Problem == Consider the following diagram. <asy> path S=polygon(4); D(S,black+linewidth(.75)); D(shift(sqrt(2),0)*S,black+linewidth(.75)); D(shift(2*sqrt(2),0)*S,black+linew...") |
m |
||
| Line 27: | Line 27: | ||
== See Also == | == See Also == | ||
{{UMO box|year=2013|before=First Problem|num-a=2}} | {{UMO box|year=2013|before=First Problem|num-a=2}} | ||
| + | |||
| + | [[Category:Intermediate Geometry Problems]] | ||
Latest revision as of 14:25, 14 October 2014
Problem
Consider the following diagram.
![[asy] path S=polygon(4); D(S,black+linewidth(.75)); D(shift(sqrt(2),0)*S,black+linewidth(.75)); D(shift(2*sqrt(2),0)*S,black+linewidth(.75)); D(shift(sqrt(2),sqrt(2))*S,black+linewidth(.75)); D(shift(2*sqrt(2),sqrt(2))*S,black+linewidth(.75)); D(shift(2*sqrt(2),2*sqrt(2))*S,black+linewidth(.75)); [/asy]](http://latex.artofproblemsolving.com/2/2/6/22630f0766979a92fa788e2b4716e7b62829e675.png)
(a) Show that you can retrace the diagram without lifting up your pencil using exactly nine (possibly overlapping) line segments.
(b) Show that you cannot retrace the diagram in the same way using eight or fewer segments.
Solution
See Also
| 2013 UMO (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All UMO Problems and Solutions | ||
