Is there an efficient way to work out how many factors a large number has?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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.
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.