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
The intention here is to find an exact expression, so rounding expressions like  "greatest integer" are not allowed.
Can you do it without using letters of any kind (x, log, lim, sum, etc.)?
As the "father" of this puzzle, I´m sure that you are recording (registering?) all the expressions achieved. All I ask of you (one of the most beautiful music ever written!!!!!) is that when we decide to stop, you send me all that we achieve, ok? I want to add this one to my files. You can find my email in "site statistics", clicking in my name.
And, as I said to you when your problem was being voted by the JM, I´m thinking in post my problem inspired in the "four fours", not totally, but some numbers hard to be found.
Posted by pcbouhid
on 2005-09-21 20:13:53