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#19 The vicar’s age

Solution

The vicar was 50 on that day (it was her birthday).

The family’s three ages must be factors of 2450 (2450 = 1 x 2 x 5 x 5 x 7 x 7). Any combination of these factors into 3 possible ages gives a product of 2450 (e.g. 2, 25 and 49), but they may give different sums when you add them (e.g. in this case 2+25+49=76).

For the bishop to be unable to figure out the exact combination of ages, there must be at least two options that you can add to make his age. Listing potential possibilities, you will find that 5, 10, 49, and 7, 7, 50 both add to 64, and this is the only pair with the same sum. Therefore 64 must be the bishop’s age.

The vicar now reveals she is older than everyone in the family, and the bishop is able to work out the family’s ages from this. If she is 51 or older, he still wouldn’t be able to tell which combination of ages the family has. But if the vicar has just turned 50, then one of the family age groups can now be eliminated – meaning the only possible family ages are 5, 10 and 49.

Quick quiz #19

Answers

1 Lifespan

2 Charm – they are the six types of quark

3 (a) 20,000. The low number came as a surprise. Before the Human Genome Project, most researchers’ best guess was around 100,000

4 The first message sent between two computers on ARPANET, the forerunner of the internet

5 Sunspots