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August 2009
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The vicar and the bell ringer - Solution
The product of the ages of the three members is 2450 = 2*5*5*7*7. The table below lists the possible ages of the members (columns 1-3) and the age of the bell ringer (column 4).

1259862
559854
1357053
1495050
577041
2254938
2353536
775032
5104932
5143527
7103526
7142523

If the bell ringer's age appeared only once in the table then he could immediately deduce the ages of the three members. However he cannot. Therefore we know that his age appears more than once in the table. The only bell ringer age that appears more than once is 32, i.e., the bell ringer's age is 32 and the ages of three members either are (7, 7, 50) or (5, 10, 49). The vicar is older than any of them. If he were 51 or older the bell ringer still would not be able to deduce the ages. However he can so the vicar's age must be 50.

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This page was last updated August 1, 2009.

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August 2009
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