Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit.

#### Grand Piano

Jack and Jill are moving into a new flat and their grand piano presents a potential problem. Fortunately, it will just pass round the corridor without being tipped or disassembled.

Given that its area, looking down from above, is the largest possible which can be passed around the corner, what is the ratio of its length to its width?

#### Cycling Digits

I have in mind a number which when you remove the units digit and place it at the front, gives the same result as multiplying the original number by 2. Am I telling the truth?

#### The Mutilated Chessboard

You are given a chessboard where two diagonally opposite corners have been removed and a large bag of dominoes of such size that they exactly cover two adjacent squares on the chessboard.

Is it possible to place 31 dominoes on the chessboard so that all the squares are covered? If yes, how? If no, why not?

#### Tennis

What is the minimum number of times a player has to hit the ball in a set of tennis and win a standard set (the set is not ended by injury, disqualification, etc.)?

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