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

Home > Numbers
Wild and Wooley Numbers (Posted on 2013-08-28) Difficulty: 3 of 5
Can 5 be written as a product of fractions in this set?

W = {2/1, 5/3, 8/5, 11/7, 14/9 ...} = {(3n + 2)/(2n + 1) : n ≥ 0}

Repetitions are allowed.

Note: Extra credit: Same question for 10 and 20.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Part 1: producing the 5. No extra credit. | Comment 1 of 2

None of the numbers containing an even number in the numerator can be used, as there would be no factor of two in any of the denominators, and therefore any integers produced would be even.

That includes 2/1--it can't be used, so the largest number from the set that can be used is the 5/3. Any number you use is at most 5/3. Even 5/3, when cubed, is less than 5, so you need at least four fractions from the set. But each fraction is more than 3/2, and (3/2)^4 is over five.

So no set can be chosen to produce a product of 5.


  Posted by Charlie on 2013-08-28 15:50:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information