### Consecutive Numbers

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

### 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.

### 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

### 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

The

This problem is taken from the UKMT Mathematical Challenges.