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

re(2): 492 please check again by brad)

it is 265 not 256

As to "good job everyone I" fully agree- also suggest that we stop here-

displaying our skills of manipulating numbers exhausted every predictable timeframe.

As to the few corections, I will email them Sunday

It is 8:25 AM here . I NEED SOME REST

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?

bye

*Edited on ***October 15, 2005, 6:56 am**