## Coin Problem

#### Problem

In my pocket I have exactly 15p, comprising of eight coins made up of 1p, 2p and 5p pieces. How many of each coin do I have?

#### Solution

As there is at least one of each type of coin, 5 + 2 + 1 = 8 (using three coins), and so the remaining (five) coins must total 15 8 = 7 pence.

7p can be made in the following ways:

5 | 2 | 2 coins | ||||||

5 | 11 | 3 coins | ||||||

2 | 2 | 2 | 1 | 4 coins | ||||

2 | 2 | 11 | 1 | 5 coins | ||||

2 | 11 | 11 | 1 | 6 coins | ||||

11 | 11 | 11 | 1 | 7 coins |

Hence 15p must be made up of one 5p, three 2p and four 1p coins.

Is it possible to have 10p in my pocket comprising of six coins and made up of 1p, 2p and 5p coins?

Problem ID: 105 (Mar 2003) Difficulty: 1 Star