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

Home > Logic > Weights and Scales
Finding Good Batteries (Posted on 2013-11-11) Difficulty: 3 of 5
My remote control needs two new batteries, but when I went to get replacements I found that the four good batteries got mixed in with four bad batteries. The only means of determining if the batteries are good is to put two into the remote and see if it works. The remote works with two good batteries and is unresponsive if I have at least one bad battery in it.

What is the minimum number of tries I need to guarantee that I get two good batteries?

See The Solution Submitted by Brian Smith    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution- | Comment 1 of 8
Answer: 22 will guarantee it .

If you  unlucky and try your batteries two by two then you may exhaust all the "bad choices" until you find a good pair.
There are 6 possibilities of getting 2 bad batteries , 4*3/2
and 16 (4*4), altogether 22 possibilities.

How to do it:  Label your batteries 1,2, ..8 . Prepare a list of all
possible un-ordered  pairings : 1&2  1&3 1&4 1&5   ...7&8, 28 at all.
Within your sequence of 22 tests, in any order, there either be "a good pair" or you have found all the bad ones, so any untested
pair (only six remaining)  qualifies.
Another reasoning :  there are only 6 good pairs if you select 2 items out of 4 (AB AC AD BC BD CD out of ABCD), so 22 tests are needed in the worst case.

  Posted by Ady TZIDON on 2013-11-11 17:04:52
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 (15)
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