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What is the smallest perfect square that ends with the four digits 9009?

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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?

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Mod 7

Find the remainder when 3^{2001} is divided by 7.

Rational Round

Age 16 to 18 Challenge Level:
The first part is simply a matter of checking the algebra.

Modulus arithmetic is useful for the second part.