12.
Here are two other arrangements of the nine digits which produce 45, their sum; each is used once only:—
5 × 8 × 9 × (7 + 2)1 × 3 × 4 × 6 = 45
72 - 5 × 8 × 93 × 4 × 6 + 1 = 45
13.
If, when the combined ages of Mary and Ann are 44, Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann, Mary is 271⁄2 years old, and Ann is 161⁄2.
For, tracing the question backwards, when Ann was 51⁄2 Mary was 161⁄2. When Ann is three times that age she will be 491⁄2. The half of this is 243⁄4, and when Mary was at that age Ann was 133⁄4. Mary’s age, by the question, was twice this, or 271⁄2.