View Full Version : My riddle...From Columbo
You enter a room with ten bags, each filled with what appears to be gold bars. Your host explains that only one bag contains real gold, and the other nine are worthless and you will get to leave with the bag of your choice.
Real gold bars weigh 11 oz., while fake gold bars weigh 10 oz.
Assume that you can not "feel" or see the difference.
Luckily, there is a scale in the room that gives weight in ounces, but it costs a penny for each use and you only have one penny.
You have one penny and ten minutes....Go...
take 1 bar from bag 1, 2 bars from bag 2, 3 from bag 3, etc.
put them all on the scale and get the total weight. it will be between 551 and 560 lbs.
If it's 551, then bag 1 is gold.
If it's 552, then bag 2 is gold.
etc...
Ray Zee
10-11-2002, 12:02 AM
great answer but i dont think you could do it in ten minutes, do you. moving all those 55 gold bars to the scale and weighing them. even if you could, then you would have all these bars probably mixed up on the scale and if it was one of the bags with the most bars taken out you wouldnt be able to tell which was which. so back to needing some luck with the good decision here. there is a spoil sport in every crowd.
lorinda
10-11-2002, 12:19 AM
You dont need to weigh bag 10, so thats only 45 bars
BruceZ
10-11-2002, 01:35 AM
...and they only weigh 10 oz. You stack them in a pyramid so you know which layer goes with which bag. No problem.
irchans
10-11-2002, 08:24 AM
What if you have two pennies, but you are worried that the scale may not be accurate with lots of weight (like over 100oz)?
BruceZ
10-11-2002, 02:49 PM
Take 1 bar each from bags 1-4, 2 bars from bag 5, and 3 bars from bag 6, and weigh these together. This will weigh at most 93 oz. If bags 5 or 6 are gold, we will find this immediately since the weight will be 93 for bag 6 and 92 for bag 5. If it weighs 91, we know one of the bags 1-4 is gold. If it weighs 90, we know none of these 4 are gold, so one of bags 7-10 are gold. In either case, we have 4 bags left to check. Set one of the 4 bags aside, and take 1+2+3 bars from the other 3 bags and weigh these together. This will be at most 63 oz, and will uniquely identify the gold bag.
Bozeman
10-11-2002, 03:03 PM
seems like you could save a little weight by only putting 2 bars from bag 6.
Craig
BruceZ
10-11-2002, 03:13 PM
Yeah, but my way I save a penny if it's in bag 5 or 6. Otherwise, both would weigh 82, and I'd have to make another measurement to determine which was gold.
The scale was said to be accurate up to 100 oz, however, if there was a chance it was inaccurate at 93 oz, then I'd be penny wise and pound foolish ha ha ha.
irchans
10-11-2002, 11:04 PM
Good Answer!
When I posed the question, I was thinking of taking 1 bar from bags 1,2, and 3, and 2 bars from bags 4,5, and 6. Your solution has a 20% of getting the right bag with one penny. My solution always used both pennies.
You place all ten bags on the scale. Insert the penny in the scale then remove the bags one at a time. Whichever bag lowers the weight by a greater amount than any other bag is the bag of gold bars. This is assuming that there an equal number of bars in each bag but there is no reason to assume otherwise given the parameters of the problem.
For those of you not old enough to remember the penny scales you were able to slowly remove weight without resetting the coin mechanism but if you tried to add additional weight they would immediately reset.
Jimbo
irchans,
My version of the solution (see my post above) saves the 2nd penny 100% of the time. Remember a penny saved is a penny earned. /forums/images/icons/smile.gif This might be a good place to mention that it is no less likely that each bag has the same numer of bars than to assume you have at least nine bars in each bag which is required for the other 1 penny solutions above. My solution requires no minimum number in each bag which I think is important.
Jimbo
baggins
10-12-2002, 05:15 AM
very nice thought process, Jimbo.
This would require the scale to be accurate over 100 oz. The 2 penny solution is for the case where we can only weigh 100 oz at a time. Also, we don't know if the bags have an equal numbers of bars.
BruceZ
10-12-2002, 09:55 AM
We could save a penny 100% of the time if we place just 1 bar from bags 1-9 on the scale, and take them off one at a time. Then we don't care how many are in each bag.
Just my 2 cents...
irchans
10-12-2002, 11:53 AM
Very true BruceZ,
I was also avoiding bumping up against the 10 minute time limit.
Jimbo
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