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Double Time
Age 16 to 18
Challenge Level 
This is another exercise in re-arranging formulae involving modulus
arithmetic and it illustrates another type of coding system.
Alternatively the pairs $(\alpha, \beta)$ can also be treated as
vectors and matrix algebra used to encode and decode the messages.
Another alternative is to use an encryption formula based on the
numbers 0 to 675 which represent the letter pairs.
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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?
