On today’s episode, shown on the Hallmark Channel, Lt. Columbo is, of course, investigating a murder. In the course of his investigation, a logic puzzle comes up. He solves the puzzle, but I think an important point was left out.
The puzzle: You are presented with bags of gold. One of the bags has “fake” gold in it. The fake gold is heavier than real gold. You have a penny scale and only one penny with which to purchase a weighing. You cannot add or remove pieces during the weighing – one penny = one reading. How do you identify the bag with the fake gold?
Columbo’s solution: Take one piece from bag 1, two pieces from bag 2, and three pieces from bag 3 (and so on). Weigh the six pieces. Suppose the real gold weighed one pound and the fake gold weighed one pound and one ounce. If all the gold pieces were real (and we know this is not true), the scale would read six pounds. If it reads six pounds and one ounce, bag 1 has the fake gold; if six pounds and two ounces, bag 2 has the fake gold; if six pounds and three ounces, bag 3 has the fake gold, and so on.
My problem: Columbo’s supposition of each real piece weighing one pound and each fake piece weighing one pound and one ounce is not in the original question. In order for Columbo’s method to work, wouldn’t you need to know the correct weights of the real and fake pieces? Since you can only weigh one time, it is not possible to make this determination.
Are the gold pieces coins, or nuggets? Columbo’s method will work if the objects are coins, or some other uniformly-sized item. For a bunch of randomly-sized gold nuggets, however, this would never work.
Still, I think that the puzzle does assume that you know the weight of a real coin. Sounds like a goof either way.
The puzzle is an old one, probably years old even when the episode was made. Columbo’s solution is correct. Possibly the dialogue misstated the puzzle. Are you sure the genius character never stated a fake coin weighs an extra ounce?
BTW, did you notice Jamie Lee Curtis in one of her earliest credited appearences?
IIRC it was stated the objects are coins. Columbo’s method will work, provided you know the relative weights of real and fake coins.
If you don’t know that there’s no way to do it. If the six coins weigh 1 exta ounce, what does that mean? Could be bag 3 is fake, and the coins are 1/3 ounce heavier.
Honestly, I was only halfway paying attention to the episode. My wife was actually watching it while I was reading the Sunday paper. Maybe I missed the statement that the gold pieces in the puzzle are coins. In Columbo’s explanation, he used gold coins (or, actually, chocolate coins). I see how the solution works, but only if you know the relative weight of the fake to real coins. I don’t see any way it works (or any other solution works) if you don’t know this.
I missed Jamie Lee Curtis. I loved how different these old detective shows are compared to modern shows like CSI. Columbo solved crimes only with his wit, not the forensic evidence. In the above episode, part of his deduction rested on scratches on the cueing arm of a phonograph. He promptly destroyed this evidence in recreating the crime for his prime suspect. The CSI guys would have gone nuts about this.
As I recall the episode Columbo was told that the real coins weighed 1 lb. and 1 oz and the fakes weighed 1 lb., or vice versa since it makes no difference.
I enjoyed the Columbo series and still do whenever I see it. However I get frustrated sometimes. In one episode Columbo wanted to find out how to get a building foundation torn down. So he went and stood in line at the the engineering department at City Hall. A Detective Lieutenant doesn’t stand in line anywhere when working a murder case. Nor do any of the detectives he has working for him.
I guess the car, the raincoat, the poor driving, the hatred of guns, the inability to hit anything with a gun, and the fact that he’s supremely effective in his current role counts against him…
Yeah. A friend of mine knows a guy who lives across the street from Columbo’s cousin. The the cousin said that he gets regular step increases in pay and doesn’t want the responsibility and politics that goes with being a Captain.
[hijack not worth its own thread]Watching “A Time to Kill” again last night, and appalled at how Charles S. Dutton slams the bloody sneaker down on the bar by the redneck guy “How did this Bloody Sneaker end up in your truck bed?!?” Why isn’t the sneaker at least in a bag or something, and why are you carrying it around town? And why does Chris Cooper tell Matthew McConnaughey all about the raped girl in front of the packed diner? Is there no attempt at confidentiality?[/hijack]
Malacandra
The correct terminology would be specific gravity. Yes, osmium does have a higher specific gravity than gold. (Osmium 22.57 vs Gold 19.32) Asterion
If the fake coins were made of osmium, they would weigh 2.7 ounces more than the 1 pound gold coins. A substance with a density of 20.53 would be required to suit the conditions of being 1 ounce heavier. (Provided I’ve done the math right).
By the way, are there any gold coins minted anywhere that weigh one pound?
Gold is going at a rate of about $680/ounce and so those one pound gold coins would be worth almost 11,000 !!! :eek:
Slight hijack here. At the end of that very episode, Theo Bikel asks Columbo another logic puzzle.
Which does not belong “uncle, asphalt, leave or delight”?
I remember which one they said it was but I believe a case could be made for any 4 of those not belonging.
If i remember correctly. the evil Mensa dude specifically tells Columbo that the only difference between the real ones and the fake ones is that the fake ones weighed more, but that it doesn’t matter by how much.
That’s what I thought, but it renders Columbo’s solution impossible.
By the way, I am totally blown away by how many people actually know this episode. Was everyone watching Hallmark Channel at the same time? I remember watching the show with my parents when I was a kid, but I couldn’t tell you any of the stories. Remember McMillan and Wife and McCloud ? Ah, the good ol’ days, when mysteries were solved with intellect, not fancy computers that don’t exist in real life.
Part of the description was how much more the fake coins weighed, he could choose any values for the real and fake coins, that’s why it “doesn’t matter”, but the values were chosen in advance. If the weight of the fakes were unknown, then the puzzle requires one more weighing, one from each bag will tell you the relative weight.
I think part of Columbo’s charm is that he doesn’t often throw his weight around like some big jerk cop, he waits patiently in line like the rest of us.