Your goal is to use the ten digits (including zero) to get as close to 1 as you can without actually getting 1.

You may use +, -, *, and /. You may combine two numbers like 4 and 7 to get 47. You may use fraction bars. You may use the numbers as powers. You may use decimals. You may use square roots, but you may only use three of them (Otherwise, you could have a near-infinite number of square roots, and the result would approach 1). You may use as many other roots as you wish, as long as you're counting the digit (i.e. if you use a cube root, that counts as your use of the digit 3). You may put a bar over part of a decimal to make it repeating. You may use a factorial, but only one.

You may not round. You may not use floor or ceiling functions. You may not use any digit more than once. You must use each digit. You may not use e, pi, etc.

Examples:

72   3   4   0
-- - - + - - - = 1.188888... (off by .1888...)
81   6   5   9

would not be as good as

57.3*4096
--------- = 0.8953125 (off by .1046875)
  (2^18)

Are we alowed to use tetration? (exponentiation is to multiplication as tetration is to multiplication.

Is 0.9 repeating = 1? Though doing something like (1+3-4)/(2+5+6+7+8) + 0.9repeating would ruin the fun anyways. I'm pretty sure most people agree that 0.999... = 1 anyways.

Hm. Come to think of it, this doesn't really contibute much. =)

I don't have an attempt that can beat the previous entries.

Posted by George on 2006-12-19 23:11:40