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

sound off about % by Josh70679)

For me it is a clear cut- do not use a % symbol

in any way. It was never intended in the original problem, it

is not a mathematical convention as an operation

and to say that 120+10%=132 befits hand calculators only.

Better stay poor (without 308) and pure than rich and

corrupted.

Take my advice = show no interest in "interest"....

Ady