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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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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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Modular Knights

Try to move the knight to visit each square once and return to the starting point on this unusual chessboard.

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?".