### 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?

# Crossing the Bridge

##### Stage: 3 Challenge Level:

Four friends need to cross a bridge.
They start on the same side of the bridge.
A maximum of two people can cross at any time.
It is night and they have just one lamp.
People that cross the bridge must carry the lamp to see the way.
A pair must walk together at the rate of the slower person:
• Rachel: - takes 1 minute to cross
• Ben: - takes 2 minutes to cross
• George: - takes 7 minutes to cross
• Yvonne: - takes 10 minutes to cross
The second fastest solution gets the friends across in 21 minutes.
The fastest takes 17 minutes. Can you work out how it is done?

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The interactivity below allows you to alter the speeds of the walkers.
Experiment with different speeds and find the fastest crossing times.

There are two optimal strategies for solving this type of problem:
Strategy 1 solves the original problem in 17 minutes
Strategy 2 solves the original problem in 21 minutes

Experiment with different speeds and work out when to use Strategy 1 and when to use Strategy 2.
Is there a way of determining in advance which strategy will be best?
Can you find sets of speeds for which both strategies give the same crossing time?

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