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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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Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Triangular Clock

Stage: 3 Short Challenge Level: Challenge Level:1

Why do this problem?

This problem offers a good opportunity for students to work systematically.

Possible approach

This is a good starter question to have on the board as students enter the room.

Key questions

  • What numbers might go next to the 12?
  • How many ways of putting the numbers on the clock might there be?

Possible extension

  • Can the numbers 1 - 13 be arranged in a circle so that the pairs add up to a triangle number?

Possible support


This problem is taken from the UKMT Mathematical Challenges.