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Millenium problem (Posted on 2006-08-21) Difficulty: 1 of 5
Write the number 1000 as an arithmetic expression, i.e. using only digits and the symbols
+ - * /
such that exactly nine 9's and no other digits show up.

See The Solution Submitted by JLo    
Rating: 3.3333 (3 votes)

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Solution a number of solutions | Comment 6 of 15 |

There may be others, but here are a few:

9999/9 - 999/9
999 + 999/999
999 + 99/99 * 9/9
999 + 9/9 * 99/99
999 + 9/9 * 9/9 * 9/9
999 + 99/99 + 9 - 9
999 + 9/9 + 9/9 - 9/9
999 + 9/9 + 99 - 99

Here are five, each using at least one each of the designated symbols:
999 + 9/9 + 9*9 - 9*9
999 + 9/9 + 9*9/9 - 9
999 + 9/9 - 9*9/9 + 9
999 + 9/9 + 9/9*9 - 9
999 + 9/9 - 9/9*9 + 9

If exponentiation is permitted, the following are also solutions:
999 + 999 / 999
999 + 999 / 999
999 + 99 / 99 * 9/9
999 + 99 / 99 + 9 - 9
999 + 999 * 99-9
999 + 999 * 9-99
999 + 99 * 9-9 * 9/9
999 + 99 * 9-9 + 9 - 9
999 + 999 / 999

Edited on August 22, 2006, 2:23 am
  Posted by Dej Mar on 2006-08-21 21:30:22

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