21 links

Question:

What is the least number of links you must cut in a chain of 21 links to be able to give someone all possible number of links up to 21?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution:  Break down the problem, because the statement of the problem has two challenges: to calculate the least number of cuts and to calculate where those cuts are to be made. The key to the solution is to find the fewest numbers that can be combined to make 21. The answer is to cut links 4 and 10. What you end up with are three sections of 3, 5, and 11 links each, plus the 2 cut links that can serve as single-link units. To give all possible number of links up to 21:

  • 1
  • 1+1
  • 3
  • 3+1
  • 5 or 3+1+1
  • 5+1
  • 5+1+1
  • 5+3
  • 5+3+1
  • 5+3+1+1
  • 11
  • 11+1
  • 11+1+1
  • 11+3
  • 11+3+1
  • 11+5
  • 11+5+1
  • 11+5+1+1
  • 11+5+3
  • 11+5+3+1
  • 11+5+3+1+1

Answer: Two cuts at links 4 and 10

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