## Half Fractions

#### Problem

By concatenating all of the digits 1, 2, 3, and 4 to form two numbers, it is impossible to find a pair that divide to make one-half. However, using the digits 1, 2, 2, and 4, it is possible to make one-half in exactly two different ways.

12 24 | = | 21 42 | = | 0.5 |

By concatenating all of the digits 1, 2, 3, 4, and 5 to form the ratio of two numbers, how many ways can you make one-half?

Problem ID: 151 (Feb 2004) Difficulty: 2 Star