1. A puzzle book challenged its readers to form an expression using five threes and basic mathematical symbols to come up with 37.
   The answer was found simply enough:
   
   33 + 3 + 3/3 = 37.
   
   Find another way to do this.
   
   
2. The same puzzle book posed the problem of finding 55 using five fours and any mathematical symbols.
   That is also easily accomplished by:
   
   44 + 44/4 = 55.
   
   Find another way to do this one, as well.

Why would you feel cheated? The problem does not say only 'fundamental' symbols are to be used which would indeed imply only the use of + = × ÷. It certainly doesn't say to find the answer that a child would most likely come up with.

Actually, the word 'basic' is only used in reference to the first part of the problem, but I think that ! and √ could be considered basic (not "fundamental") operations anyway, as opposed to trigonometric or calculus operators.

In any case, I think factorial and square root would be allowable, but I'm not especially fond of considering a decimal point to be a mathematical symbol in this context (or, consequently, the bar for a repeating decimal).

So, these are the rules, if a little late:
Good symbols:
+, -, ×, ÷ (fundamental arithmetic); !, √ (other basic operations); || (absolute value)

Bad symbols:
sin, cos, tan (trig functions); floor, ceil (rounding); .¯ (decimals and repeating digits), e, π (mathematical constants)

By the way, exponentiation is not a symbol at all, but since 3³ uses only the two digits, it's perfectly fine. Don't know how that's useful here, though...

Posted by DJ on 2003-08-29 16:17:48