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.
Other articles on this blog on similar themes:
Snakes and Ladders (A look at the Collatz Conjecture)Crafty Calculator Calculations (numerical anagrams with five digits)
More Multiplications (numerical anagrams with four digits)
Over and Out (reduce large numbers to zero as efficiently as possible)
Calculator Games: Front to Back
Calculator Games: The Kaprekar Constant
Other articles in the 'A Puzzle A Day' series:
Three Horse RaceHow Old is Aunt Tabitha
Big Ben Strikes Twelve
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