Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CR: Review Problem Set
Problem 35CR
See similar textbooks
icon
Related questions
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.
Transcribed Image Text: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.
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS