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14 Divisors

What is the smallest number with exactly 14 divisors?

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Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Emptied Cube

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

The sculpture 'Cubo Vazado' [Emptied Cube] by the Brazilian artist Franz Weissmann is formed by removing cubical blocks from a solid cube to leave the symmetrical shape shown.

If all the edges have length $1$, $2$ or $3$ units, what is the volume of the sculpture and what is its surface area?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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