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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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Sixational

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.

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Telescoping Functions

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

Factorial Fun

Age 16 to 18 Challenge Level:

Trying the problem for small values of $n$ is a good problem solving strategy. Here you might try $n = 2, 3$ and $4$.

The parts of the question are stepping stones leading you to answering the question "How many factors does $n!$ have?".