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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?

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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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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?

Crossing the Bridge

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

Why do this problem?

I've set this as an introductory problem to a day's workshop on Problem Solving. Students reaction has often been "It's impossible!"

Once the problem was solved it provided a useful vehicle for discussing what mathematicians do when they are stuck: experiment, explore dead ends, discuss with friends, walk away from the problem and return to it later...

Teachers may want to use this problem to help students think about what they do when they want to give up.