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A A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches.

A A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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What are the numbers of matchesticks you can have in the box so that you can make all possible pairs of the given shapes using all the matchsticks in each pair? 

A A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches.
Transcribed Image Text:A A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches.
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