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Pastimes : Laughter is the Best Medicine - Tell us a joke -- Ignore unavailable to you. Want to Upgrade?

To: Bob Bryenton who wrote (8997)	3/17/1999 9:20:00 AM
From: William B. Kohn	Read Replies (2) \| Respond to of 62549

Coin question. Answer I think is three Bill

To: Bob Bryenton who wrote (8997)	3/17/1999 9:36:00 AM
From: Graham C.	Respond to of 62549

Coins on the balance : solution ... . . ( actually , the version I heard before was billiard/ snooker/pool balls ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The solution makes perfect sense - but is extremely difficult to express concisely. 1. Weigh 4 against 4. There are two outcomes possible 1A - they balance => all eight are normal : mark them N 1B - they don't balance => either one on the light side is lighter, or one on the heavy side is heavier : mark 4 H and the other 4 L If outcome of 1 is A, weigh three of the remaining 4 against three of the N's. This time there are three possible outcomes :- 1A2A - They balance; then the last remaining one is odd. Simply weigh it against any normal one to determine whether it is heavier or lighter. 1A2B - The unknowns are heavier than the N's. ( This means the 12th one is normal and one of these three unknowns is heavier. ) The weight two fo these three against each other. There are two outcomoes :- 1A2B3A - they balance - then the third one is Heavy. 1A2B3B - one is heavier than the other - so that is the Heavy one. 1A2C - ditto 1A2B solution changing Heavy to Light etc. If the outcome of 1 is B - they don't balance, then you have 4 L's ( one of which MAY be lighter ), 4 H's ( one of which MAY be heavier ) and the remaining 4 are normal N's. Here's the tricky bit ... Weigh L+L+H against L+H+N, giving three possible outcomes :- 1B2A - they balance. So the odd one is one of the remaining L, H or H. Weight H against H and either one will be truly Heavy or else they will balance leaving the odd L as the Light odd one. 1B2B - the L+L+H side is heavier. So either this H is truly Heavy, or the L on the other side is truly light. So weigh one of those against any normal one - if it doesn't balance, it is the odd one; if it does balance, the other one is the odd one. 1B2C - the L+L+H side is lighter. Weight the L against the L - if they balance, the H on the other side is truly Heavy; if they don't balance, the lighter one of them is truly Light. Clear ? As mud.