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#251 Children of Quirkopia

Set by Zoe Mensch

For an inexplicable reason, the population on the island of Quirkopia had always been split 75 per cent male and 25 per cent female. Maybe it is genetic, or maybe it is something in the water. Anyway, the new president of the island believed something should be done about it, so she decided to implement a new family planning policy.

From then on, families were allowed to have as many children as they wanted until they had a boy, at which point they had to stop. There was no obligation to keep having children of course 鈥� parents might have two girls and finish there.

Fifty years later, you visit the island鈥檚 school. As the children filter back into the classroom, what do you notice?

a) They are all boys

b) About three-quarters are boys

c) The class is split roughly 50/50 boys and girls

d) There are more girls than boys

Solution next week

#250 Are we nearly there yet?

Solution

The journey will take a further 16 minutes. Call the first and last digits of the original distance a and b. We know the middle digit was zero, so that distance was a0b. As the speed is constant, the distances covered in the two 45-minute periods must be equal, so that a0b 鈥� ba = ba 鈥� ab, which gives a0b + ab = 2(ba).

A number written as 鈥渁0b鈥� equates to 100a + b and ab to 10a+b. So our equation becomes 100a + b + 10a + b = 20b + 2a. This gives 108a = 18b. Hence b = 6a. Since b is a single digit, it must be 6 and a =1. The distances were 106, 61 and 16 and, with 45 miles taking 45 minutes, the final 16 miles take 16 minutes.