perplexus.info :: Weights and Scales : Tricky Pearls

Tricky Pearls (Posted on 2002-10-08)

You have been given 10 bags of pearls. You are told that one of the bags is full of those cheap plastic kind of pearls, but the other nine are the real deal. Naturally, you cannot tell the difference just by looking. However, you know that the fake pearls weigh 9 grams each, while the real ones are one gram heavier and weigh 10.

Armed with a very presice scale, you could weigh a pearl from each bag until you find the fake one by weight, but that would take up to 10 weighings. Can you do it in less?

Submitted by levik

Rating: 3.7778 (9 votes)

Solution: (Hide)

Take a pearl from bag 1, 2 pearls from bag 2, 3 pearls from bag 3, etc.
Weigh this pile of pearls you have. If they were all real, the result would weigh 10*(1+2+3+4+...+10) = 550 grams.
Because some of the pearls are fake, your result will be less.
If it's one gram less, then the bad pearls are in bag 1. If the difference is 2 grams, then bag #2 is the culptit, etc.
Thus the problem is solvable in one weighing.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-06-18 23:12:12
cheap way	humfoozneydannle	2005-01-02 00:50:23
Colombo	Bruce Brantley	2004-09-01 05:19:56
No Subject	Gamer	2003-04-08 12:40:36
Chance	N__A__T__A	2003-01-02 10:57:53
re(4): Question of a question	Nick Reed	2002-10-09 06:40:46
re(3): Question of a question	levik	2002-10-09 01:32:53
re(2): Question of a question	Nick Reed	2002-10-08 22:30:50
re(3): Solution	TomM	2002-10-08 18:40:28
re: Question of a question	TomM	2002-10-08 18:33:44
re(2): Solution	TomM	2002-10-08 18:27:22
Question of a question	Nick Reed	2002-10-08 11:43:54
possible soultion	Amanda	2002-10-08 09:10:29
re: Solution	friedlinguini	2002-10-08 06:25:36
Solution	Rich Cowley	2002-10-08 05:40:17

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