The Age of the Vicar (Puzzle)

by Alan Sykes

A vicar says to his curate:

“I have three parishioners whose ages multiply together to equal 2450 and whose ages sum to twice your age – what are the ages of the parishioners?”

The curate thinks for a while and then tells the vicar that he does not have enough information. “Quite right” replies the vicar “but if I tell you an extra piece of information you will have enough.” The extra piece of information is that the vicar is older than any of his parishioners.

Your task is to find the age of the vicar!

Solution

Since 2450 equals 2.5.5.7.7 you can work out a list of possible ages of the parishioners, which in increasing order of ages is:

2 25 49 
2 35 35 
5 10 49 
5 14 35 
7 7 50 
7 10 35 
7 14 25

The curate (naturally) knows his own age. These sets of numbers add up to 76 72 64 54 64 52 and 46 respectively, and so the curate’s age is 32 and the possible sets of ages are 5 10 49 or 7 7 50, as 64 is the only number that is repeated.

The curate is told that the knowledge that the vicar is older than any of his parishioners is sufficient information for him to decide what the ages of the parishioners are. This can only be the case if the vicar is 50 – if he were 51 or more, you would not be able to choose between the two possible sets of ages!

Hence the curate is 32, the parishioners are 5 10 and 49 and the vicar is 50!