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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?

Weekly Problem 31 - 2007

Stage: 3 Challenge Level: Challenge Level:1

By subtracting 12 from our list of triangle numbers, 3 and 9 must be either side of the 12, and so we will choose to place the 3 on the right. We can keep doing this to get the following:
Clock: going clockwise 12, 3, 7, 8, 2, A, B, C, D, E, F, 9
By the same reasoning A is either 1 or 4, and F is either 1 or 6. But if F=1, then E=4, and so F=6, but 11+6=17 is not a triangle number. So F is not a 1, and so must be a 6.
So E=4, A=1, and so D=11, C=10 and B=5.

This problem is taken from the UKMT Mathematical Challenges.

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