Able, Gifted & Talented at Hadleigh High School
IMPOSSIBLE MATHS PUZZLES
We have found nine puzzles to leave you chewing your pencil and pulling out your hair....
(Answers at the bottom - don't cheat!)
1) The parked car puzzle:
All you have to do is say what number is under the parked car.
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2) How to beat Roger Federer at Wimbledon:
Thanks to a set of temporary magical powers you are in the final of the Wimbledon tennis championships up against seven-time winner Roger Federer. Your powers cannot last for the whole match and you must therefore choose the optimum time for them to run out. What is the score that gives you the maximum chance of winning?
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3) Get the olive out of the martini glass:
You must rearrange these matchsticks so that the olive (that's the thing in the middle) is removed from the Martini glass. The olive must not be touched and you are only allowed to move two of the matchsticks. The Martini glass can be turned onto its left or right side, or even upside down, but must remain in the exact same shape.
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None of these images are the solution because the olive is still inside the glass or because the glass has taken a different form....
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4) Draw one line on this equation to make it correct:
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5) 1000 school lockers:
There is a school with 1,000 students and 1,000 lockers. On the first day of term the headteacher asks the first student to go along and open every single locker, he asks the second to go to every second locker and close it, the third to go to every third locker and close it if it is open or open it if it is closed, the fourth to go to the fourth locker and so on. The process is completed with the thousandth student. How many lockers are open at the end?
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6) Crazy cut:
Add one cut (or draw one line), which doesn't need to be straight, that can divide this shape into two identical parts.
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7) Coloured socks puzzle:
You are getting dressed in the dark and realise that you forgot to bind all your socks together into pairs. However you know there are exactly 10 pairs of white socks and 10 pairs of black socks in your draw. All the socks are exactly the same except for their colour. How many socks do you need to take with you to ensure you have at least a pair that match?
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8) Rays through the squares:
Can you prove that angle C is the sum of angles A and B?
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9) Love in Kleptopia:
John and Mary have fallen in love. John wants to send Mary a ring through the post but in their country of Kleptopia, any package that is not locked will have its contents stolen. John and Mary have plenty of padlocks but neither has the other's key. How can John get the ring safely to Mary?
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So how did you do?
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1) The parked car puzzle:
Try looking at the picture upside down.....
The answer is 87.
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2) How to beat Roger Federer at Wimbledon:
6-0, 6-0, 6-6 (*6-0)
The obvious answer here would be to be two sets up, five games up and winning 40-0 (ie. 6-0, 6-0, 5-0 (*40-)). That would give you three chances of winning the one point you need in the best of five set match.
However, to provide you with the best chance of winning, you should be two sets up, with the third set drawn at 6-6 and then 6-0 up in the third set tie break. This would give you six chances to win the one point you need.
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3) Get the olive out of the martini glass:
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4) Draw one line on this equation to make it correct:
You simply need to turn the 2nd + into a 4
5+545+5+5=555
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5) 1000 school lockers:
The only lockers that remain open are square numbers (1,4,916,25, etc) because these are the only numbers divisible by an odd number of numbers. Therefore they will be changed by an odd number of students and left open at the end.
Each number with a square root of 31 (961) or fewer will be left open (the square of 32 (1024) is greater than 1000 and therefore out of the range.
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6) Crazy cut:
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7) Coloured socks puzzle:
Answer = 3. If you pull out just two socks it is possible you will have one black sock and one white sock. However, if you pull out a third you are guaranteed to have a matching pair - either with three of the same colour or one odd one out.
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8) Rays through the squares:
Create two new squares (shown overlapped). We know that the sum of A and D is the same as C because it is created by splitting a square diagonally. Angle B must be the same as D because it is the corresponding angle of a similar right-angle triangle (made from cutting a rectangle). That means B can be substituted for D and thus the sum of A and B is the same as C.
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9) Love in Kleptopia:
John should send Mary the ring in a package with a padlock on it. Mary can then attach her own padlock and send it back to John. John then takes his own padlock off, sends the package, which still has Mary's padlock on it, back to her and voila!
