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A piece of string is cut into five pieces.
Each piece is an exact number of centimetres long. None of the pieces are the same lengths and none of the lengths are multiples of any of the other lengths.
If the smallest piece is 2cm long, what is the shortest possible length of the original piece of string?
Solution:
To solve this problem you can simply work systematically upwards from 2cm using each length that is not a multiple of previously used lengths. The table below shows how this could be recorded.
| Length | Multiple of | Can it be used? |
| 3cm | none | Yes |
| 4cm | 2cm | No |
| 5cm | none | Yes |
| 6cm | 2cm and 3cm | No |
| 7cm | none | Yes |
| 8cm | 2cm and 4cm | No |
| 9cm | 3cm | No |
| 10cm | 2cm and 5cm | No |
| 11cm | None | Yes |
You should notice that the lengths are the first five prime numbers.
Adding together the five lengths we find that the original piece of string was 2cm + 3cm + 5cm + 7cm + 11cm, or 28cm long.