PUZZLE 3- from the 19th to the 25th October (to be collected by the 26th October)
A NUMEROUS FAMILY
The product of my sons’ ages is 1664. The age of the eldest is the double of my youngest son’s age. I am 50 years old myself.
How many sons have I got?
How old are they?
The factorial decomposition of 1664 is the product of 13 x 2 with exponent 7. Since 13 can be neither the youngest nor the eldest son, the solution is 2 with exponent 3 = 8, 13, and 2 with exponent 4 = 16. Therefore the three sons are: 8, 13 and 16 years old.