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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?

Inscribed Hexagon

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

As the sum of the angles in a triangle is 180° and all four angles in a rectangle are 90°, then sum of the two marked angles in the triangle 180° - 90° = 90°.
Each interior angle of a regular hexagon is 120° and the sum of the angles in a quadrilateral is 360°; hence the sum of the two marked angles in the quadrilateral is 360° - 90° - (360° - 120°) = 30°.
Hence the sum of the four marked angles is 90° + 30° = 120°.

This problem is taken from the UKMT Mathematical Challenges.
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