Triangle In A Bag
Geometry
Level
2
A bag contains 100 measuring sticks, each one a different integer length from 1 to 100 cm. What's the maximum number of sticks that you can leave in the bag so that any three of the remaining sticks can be held up end-to-end to make a triangle?
51
25
50
100
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1 solution
You want to keep the long sticks, as more of them will fit into a given ratio, such as between full length and a half of that. So the longest will be 100. The shortest two will have to make more than 100 together. That makes the shorter of those two at least 50. Counting from 50 to 100 there are 51 sticks.