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

 Twelve Coins and a Broken Scale (Posted on 2005-06-24)
You have 12 coins, six weigh 24 grams and six weigh 25 grams. You also have the broken scale from Five Weights and a Broken Scale.

Sort the 12 coins into the group of 24g coins and the group of 25g coins using that broken scale no more than 9 times.

 Submitted by Brian Smith Rating: 3.3333 (3 votes) Solution: (Hide) At most nine weighings are needed as follows. Note: I will refer to the 25g coins as heavy coins and 24g coins as light coins. Divide the coins into four groups (A,B,C,D) of 3 coins. Take three weighings: AB vs CD, AC vs BD, and AD vs BC By taking 6 vs 6 for the initial weighings, if two groups are different, there is enough of a difference(2g+) for the broken scale to sense it. Case 1: None of the weighings are equal One of the groups is always on the heavy side or always on the light side of the weighings For example, if the weighings were AB>CD, ACBD, ADXZ then Y is heavy and X and Z are light. If the results are KX>YZ and KY=XZ then X is heavy and Y and Z are light. Repeat the procedure for the other two mixed groups. Total weighings: 9 Case 1.2:One group of three is always light This is identical to Case 1.1 with heavy and light switched around. Also total weighings: 9 Case 2: Exactly one weighing is equal One group is three heavy coins, one group is three light coins, one group is two heavy and one light coin and one group is one heavy and two light coins. If the weighings were AB>CD, AC

Comments: ( You must be logged in to post comments.)
 Subject Author Date Fixed solution... Cougar Draven 2005-07-05 22:18:19 Solution (by Visual Basic program) Penny 2005-07-03 19:19:24 Solution (By Ed Mekler and Chris Longfellow Chris Longfellow 2005-07-02 22:18:43 Solution =) Eugene 2005-06-30 06:34:55 Some thoughts owl 2005-06-30 04:06:21 re(2): Solution, I think. Penny 2005-06-28 14:13:53 re: Solution, I think. Federico Kereki 2005-06-26 01:34:23 Solution, I think. Cougar Draven 2005-06-25 22:44:59

 Search: Search body:
Forums (0)