### Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

### Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

### Old Nuts

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?

# 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.