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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?

Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:1

Warmsnug calculate the prices of their windows according to the area of glass used and the length of frame needed.

Can you work out how Warmsnug arrived at the prices of the windows below?
Which window has been given an incorrect price?

windows

The information is available on a printable worksheet here.

This spreadsheet generates prices for the windows according to different pricing rules.
Can you find an efficient strategy for finding how the prices were calculated?


This problem is based on the original Warmsnug Double Glazing problem which appeared in The Language of Functions and Graphs produced by the Shell Centre for Mathematical Education and the Joint Matriculation Board.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.