Puzzles
MathsJam
Source: @samholloway on Twitter
Maths Jam is always held on the second-to-last Tuesday of the month. This month, it will be held on the 17th. What is the earliest date in the month on which Maths Jam can fall and when will this next happen?
Pocket money
When Dad gave out the pocket money, Amy received twice as much as her first brother, three times as much as the second, four times as much as the third and five times as much as the last brother. Peter complained that he had received 30p less than Tom.
Use this information to find all the possible amounts of money that Amy could have received.
Always a multiple?
Source: nrich
Take a two digit number. Reverse the digits and add the result to your original number. Your answer is multiple of 11.
Prove that the answer will be a multiple of 11 for any starting number.
Will this work with three digit numbers? Four digit numbers? \(n\) digit numbers?
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.)?
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?
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?
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.
![](javascript:showlimage("piano.png"))
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?
![](javascript:showlimage("piano-ans.png"))
![](javascript:showlimage("piano-ans2.png"))
Superdog
Source: Futility Closet
A dog is running along a beach at 2m/s. The dog's owner blow a whistle every 10 seconds. Each time the dog hears a whistle, she doubles her speed. How many whistles will the dog hear?
(Hint: speed of sound = 343m/s)
(Hint 2: The answer is not eight!)