All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Five Fives (Posted on 2005-09-18)
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.)?

 Submitted by Josh70679 Rating: 4.4737 (19 votes) Solution: (Hide) 37 = .5^(-5) + 5. Other creative solutions can be found in the posts. Bonus: Can you find expressions for 1 thru 30? How many consecutive positive integers can you express? Our record is 291. Can you do better?? This is one of my all-time favorites. I'm pleased by all the great work people have done on this problem. Thanks to everyone who contributed.

 Search: Search body:
Forums (0)