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Purr-fection
Age 16 to 18
Challenge Level 
Try to be systematic. How can you narrow down the cases to be tested?
If the last digit of a square number is 9 what can you say about the number?
Can you write down an expression for a number using its digits and powers of 10?
Possible support
Note: Other problems using modulus arithmetic: Dirisibly Yours , Obviously, Rational Round
An article that explains the basic ideas of modulus arithmetic: Modulus Arithmetic and Solution to Dirisibly Yours.
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In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
