Find seven different unit fractions whose sum is 1.

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Problem

Find seven different unit fractions whose sum is 1.

1   1   1   1   1   1   1
- + - + - + - + - + - + - = 1
a   b   c   d   e   f   g

The denominators must be positive whole numbers.

-- CrACKeD <cracked@primenet.com>

Show solution

There are probably many solutions, but observing that

1/2 + 1/3 + 1/6 = 1

1/2 + 1/3 + 1/6 * 1 = 1

1/2 + 1/3 + 1/6 * (1/2 + 1/3 + 1/6) = 1

1/2 + 1/3 + 1/12 + 1/18 + 1/36 = 1

1/2 + 1/3 + 1/12 + 1/18 + 1/36 * 1 = 1

1/2 + 1/3 + 1/12 + 1/18 + 1/36 * (1/2 + 1/3 + 1/6) = 1

1/2 + 1/3 + 1/12 + 1/18 + 1/72 + 1/108 + 1/216 = 1

[ Editor: the rec.puzzles oracle's reply to the poster, October 1996. ]

1   1   1   1   1   1   1
- + - + - + - + - + - + - = 1
3   4   8   9  12  18  24

-- Bill Shatzer <bshatzer@orednet.org>