Puzzle 84:
Mr Puzzle says there is only one unique set of three numbers whose total (added together) is equal to their product (multiplied together). What is it?
This puzzle reminds me of the recent question - "What three numbers satisfy 1/a + 1/b + 1/c = 1?", where the answer was 1/2 + 1/3 + 1/6 = 1.
The answer to a + b + c = abc can be found if you know that 6 is a 'magic' number - the sum of its factors is equal to their product.
The factors of 6 are 1, 2 and 3: 1 + 2 + 3 = 6 = 1 * 2 * 3
6 is a perfect number - it's equal to the sum of its divisors (except itself). Another example is 28 (1 + 2 + 4 + 7 + 14); there are plenty more perfect numbers, and they are extremely large.
6, also is a magic number - it's equal to the product of its divisors (again, except itself). I can't find any other examples - I guess 6 is unique. Well, that's what Mr Puzzle said, anyway.
Mr Puzzle says there is only one unique set of three numbers whose total (added together) is equal to their product (multiplied together). What is it?
This puzzle reminds me of the recent question - "What three numbers satisfy 1/a + 1/b + 1/c = 1?", where the answer was 1/2 + 1/3 + 1/6 = 1.
The answer to a + b + c = abc can be found if you know that 6 is a 'magic' number - the sum of its factors is equal to their product.
The factors of 6 are 1, 2 and 3: 1 + 2 + 3 = 6 = 1 * 2 * 3
6 is a perfect number - it's equal to the sum of its divisors (except itself). Another example is 28 (1 + 2 + 4 + 7 + 14); there are plenty more perfect numbers, and they are extremely large.
6, also is a magic number - it's equal to the product of its divisors (again, except itself). I can't find any other examples - I guess 6 is unique. Well, that's what Mr Puzzle said, anyway.
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