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 What is the minimum possible number of matches 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? Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.

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 What is the minimum possible number of matches 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? Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.

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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Question

I know the minimum number is 36. So please skip that question and I really want to know "If you consider some other shapes with different number of sides, is there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes?"

9. A regular problem
스
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.
What is the minimum possible number of matches 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?
Consider some other shapes with different number of sides. IS there a general rule to relate
the number of matchsticks to make all the pairs and the number of sides in the shapes.

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