Making Maths Count

Maths Week Scotland – Coinage System

September 15, 2018 by 1 Comment

Welcome to the day six Maths Week Scotland 2018 puzzle. You might want to work together with friends or family members to solve this one. Enjoy! You can find the solution to this and all of the rest of the puzzles here tomorrow.

Coinage System

The imaginary country of Gaussland decides to adopt a new system of coinage. There are to be coins of ten different values (denominations). Those values (in cents) are:

  • 1, 3, 6, 10, 15, 21, 28, 36, 45, 55.

The idea is that by changing to the new system it will be possible to pay for any item up to the value of 99 cents using no more than three coins. For example:

  • 5=3+1+1
  • 51=45+6

Show how no more than three coins can be used for each amount to 99 cents or, if this is not the case, find the smallest amount for which four coins are needed.


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