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## Sunday, 20 April 2014

### Sunday Afternoon Maths IX

Here's this week's collection. Answers & extensions here. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit. This Tuesday is Maths Jam, make sure you're there!

#### Equal Areas

An equilateral triangle and a square have the same area. What is the ratio of the perimeter of the triangle to the perimeter of the square?

#### Chessboard Squares

It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?

#### Downing Street

A knot of spectators in Downing Street was watching members of the Cabinet as they arrived for a critical meeting.
"Who's that?" I asked my neighbour, as a silk-hatted figure, carrying rolled umbrella, rang the bell at No. 10. "Is it the Minister of Maths?"
"Yes," he said.
"Quite right," said a second spectator. "The Minister of Maths it is. Looks grim, doesn't he?"
The first of the speakers tells the truth three times out of four. The second tells the truth four times out of five.
What is the probability that the gentleman in question was in fact the Minister of Maths?

#### Multiple Sum

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.