jsgray@watmath.UUCP (Jan Gray) (04/13/85)
Here's a different "weighing problem", stolen from a "Columbo" from years gone by... You are given, say, 100 bags of 100 coins each; one of the bags contains counterfeit coins, which weigh, say, 10% less than the real coins. You must determine, in ONE weighing, which bag contains the counterfeits. I'll post the solution in one week. Jan Gray (jsgray@watmath.UUCP) University of Waterloo (519) 885-1211 x3870
js2j@mhuxt.UUCP (sonntag) (04/15/85)
> Here's a different "weighing problem", stolen from a "Columbo" from > years gone by... > > You are given, say, 100 bags of 100 coins each; one of the bags contains > counterfeit coins, which weigh, say, 10% less than the real coins. > You must determine, in ONE weighing, which bag contains the counterfeits. > > I'll post the solution in one week. > > Jan Gray (jsgray@watmath.UUCP) University of Waterloo (519) 885-1211 x3870 Easy! Just pile up 1 coin from bag #1, 2 coins from bag #2, ..., and 100 coins from bag #100. Weigh the entire pile together. Subtract this weight from the weight of (100 triangular (100+99+98+..+1)) real coins. Divide this difference by the difference in weight between real and counterfiet coins. The result is the number of the bag containing the counterfiet coins. I'm assuming that you know pretty accurately just what a single real coin and a single counterfiet coin weigh. -- Jeff Sonntag ihnp4!mhuxt!js2j "In the long run, we'll all be dead."-John Maynard Keynes
pankaj@sbcs.UUCP (Pankaj Gupta) (04/16/85)
> Here's a different "weighing problem", stolen from a "Columbo" from > years gone by... > > You are given, say, 100 bags of 100 coins each; one of the bags contains > counterfeit coins, which weigh, say, 10% less than the real coins. > You must determine, in ONE weighing, which bag contains the counterfeits. > > Jan Gray (jsgray@watmath.UUCP) University of Waterloo (519) 885-1211 x3870 Take 1 coin from bag 1, 2 coins from bag2, ............ 100 coins from bag 100 and find the total weight from which you can deduce which bag contained the counterfeits.
riks@athena.UUCP (Rik Smoody) (04/18/85)
> > You are given, say, 100 bags of 100 coins each; one of the bags contains > > counterfeit coins, which weigh, say, 10% less than the real coins. > > You must determine, in ONE weighing, which bag contains the counterfeits. > > Easy! Just pile up 1 coin from bag #1, 2 coins from bag #2, ..., and > 100 coins from bag #100. Weigh the entire pile together. Subtract this > weight from the weight of (100 triangular (100+99+98+..+1)) real coins. > Divide this difference by the difference in weight between real and > counterfiet coins. The result is the number of the bag containing the > counterfiet coins. > > I'm assuming that you know pretty accurately just what a single real > coin and a single counterfiet coin weigh. I have used this as an example of the difference between puzzle solving and problem solving. The mathematics is easy, but the pragmatics of counting out those coins and keeping track of exactly which 37 coins came from bag 37, etc, makes the clever solution rather impractical. Do you really expect some bloke from the FBI to be able to count to 50? And divide yet? Cheers, Rik Smoody
js2j@mhuxt.UUCP (sonntag) (04/23/85)
> > > You are given, say, 100 bags of 100 coins each; one of the bags contains > > > counterfeit coins, which weigh, say, 10% less than the real coins. > > > You must determine, in ONE weighing, which bag contains the counterfeits. > > > > Easy! Just pile up 1 coin from bag #1, 2 coins from bag #2, ..., and > > 100 coins from bag #100. Weigh the entire pile together. Subtract this > > weight from the weight of (100 triangular (100+99+98+..+1)) real coins. > > Divide this difference by the difference in weight between real and > > counterfiet coins. The result is the number of the bag containing the > > counterfiet coins. > > > > I'm assuming that you know pretty accurately just what a single real > > coin and a single counterfiet coin weigh. > > I have used this as an example of the difference between puzzle solving > and problem solving. > The mathematics is easy, but the pragmatics of counting out those coins > and keeping track of exactly which 37 coins came from bag 37, etc, > makes the clever solution rather impractical. > > Rik Smoody Who said anything about keeping track of which coins came from which bag? Certainly not me. I was just planning on dumping them into one big pile. Do you understand how this solution works? -- Jeff Sonntag ihnp4!mhuxt!js2j "But if we took out the bones, it wouldn't be crunchy, now, would it?"