PUZZLES
1) A woman with three daughters passes her neighbour’s house. The neighbour asks the daughters’ ages. The woman answers that their ages multiplied together is 36, and their ages added together is the same number as his address. The neighbour stares at his address. The woman then says she forgot to mention an essential piece of information. The information is that her eldest daughter’s name is Jenny. The neighbour now is able to determine the daughters’ ages. How does the neighbour do it? (NB We’re dealing only with whole integer ages.)
2) Here’s a classic alphametric from 1924. What numbers do the letters stand for?
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MONEY
The answers to last month’s puzzles were supplied last month.
Here are the answers to this month’s puzzles:
1) The man makes a chart of the possible ages, consisting of the three numbers whose combined product is 36.
| Daughter A’s Age | Daughter B’s Age | Daughter C’s Age | Sum of Ages |
| 1 | 1 | 36 | 38 |
| 1 | 2 | 18 | 21 |
| 1 | 3 | 12 | 16 |
| 1 | 4 | 9 | 14 |
| 1 | 6 | 6 | 13 |
| 2 | 2 | 9 | 13 |
| 2 | 3 | 6 | 11 |
| 3 | 3 | 4 | 10 |
There is only one case in which the neighbour needs additional information, and that is if the sum of the ages is 13. The neighbour concludes that when the woman gave the essential information it was to differentiate between the two cases where the sum is 13. The statement that the woman’s eldest daughter’s name is Jenny means that there is only one eldest daughter. This eliminates the possibility of twins age 6. The three ages are therefore 2, 2, and 9.
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