A mathematician who was exceedingly fond of the number five set to work trying to express as many consecutive integers using no numerals besides '5', and only up to five of them. She allowed herself to use any standard mathematical notation she knew, as long as it didn't contain any numerals. For example, she could use the symbol for 'square root', but not 'cube root' (because it contains a '3'). She determined that the highest consecutive integer she could express this way was 36. Her last few calculations were as follows:

• 31 = 5*5 + 5 + (5/5)
• 32 = 55*.5 + 5 - .5
• 33 = (55 + 5) * .55
• 34 = 5!/5 + 5/.5
• 35 = (5 + (5+5)/5) * 5
• 36 = 5*5 + 55/5
• 37 = ?

Was she correct in thinking 36 was the highest consecutive integer she could express this way? Can you express 37 using only up to five 5's?

Note: The intention here is to find an exact expression, so rounding expressions like [] "greatest integer" are not allowed.
Note: Can you do it without using letters of any kind (x, log, lim, sum, etc.)?

(In reply to % by brad)

Brad, read the second note of the problem.

We are trying, since the beginning to avoid any kind of symbols that is not a "standard mathematical notation", and letters.

I suggested, in my first comment, the function "termial", denoted by "?", that is considered a standard math notation. 

But, in spite of this, we tried to avoid it, and we could reach 300 and much more.

Think in a tool like 5? = 15 (15 with only one five)!

Posted by pcbouhid on 2005-10-11 13:21:12