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.

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 + 9}9⁹ _{/ 9}9⁹

Edited on August 22, 2006, 2:23 am

Posted by Dej Mar on 2006-08-21 21:30:22