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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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14 Divisors

What is the smallest number with exactly 14 divisors?

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Summing Consecutive Numbers

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?

Extended Parallelogram

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

Opposite angles of a parallelogram are equal, so ∠QPS = 50°. Therefore, ∠QPT = 112° and, as triangle QPT is isosceles, ∠PQT = (180°-112°)/2=34°. As PQRS is a parallelogram, ∠PQR = 180° - 50° = 130°.

So ∠TQR = 130° - 34° = 96°.

This problem is taken from the UKMT Mathematical Challenges.
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