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

Home > Numbers
Bananas (Posted on 2006-08-28) Difficulty: 2 of 5
100 monkeys have together 1600 bananas. Show that at least four monkeys have the same number of bananas.

  Submitted by JLo    
Rating: 3.3333 (3 votes)
Solution: (Hide)
Consider the first 99 monkeys. The least number of bananas that does not give 4 monkeys the same amount, is distributed such that monkey 1,2,3 get nothing, monkey 4,5,6 get one banana, monkey 7,8,9 get two and so forth. We end up distributing 3*33*32/2 = 1584 bananas. That leaves 16 bananas for the monkey #100, an amount that has already been given to 3 others. If we only had 17 bananas more we could give 33 bananas to #100 and we'd be fine.

See also Old Original Oskar!'s posting (1617 reasons...)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2022-07-23 07:56:52
re(3): My morning breakfast (sanity is restored)JLo2006-09-01 13:30:05
re(2): My morning breakfast (sanity is restored)Steve Herman2006-09-01 13:08:49
Some Thoughtsre: The answer is simpleOld Original Oskar!2006-08-30 22:08:27
The answer is simpleCraig2006-08-29 20:52:34
Some Thoughtsre: AnswerOld Original Oskar!2006-08-29 13:14:23
SolutionAnswerGiorgio Rivieccio2006-08-29 05:42:19
Answer (Practically)Vernon Lewis2006-08-28 11:54:16
Questionre: My morning breakfastJLo2006-08-28 11:21:47
Some ThoughtsMy morning breakfastSteve Herman2006-08-28 10:56:52
Solution1617 reasonsOld Original Oskar!2006-08-28 09:47:30
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 (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information