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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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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?

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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

The Patent Solution

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

This is quite a challenge and it is really a magic square in disguise! Here is one solution and another similar puzzle for you to try. You may like to study the articles Magic Squares and Magic Squares II.

Patent Solution solution

Patent Solution Solution

Another Patent Puzzle - again the magic total is 132

The following puzzle comes from The Ultimate Book of Number Puzzles by Kenneth Kelsey published by The Cresset Press 1992, ISBN: 0 09 177204 4.

Another Patent Puzzle