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...

Re: My riddle...From Columbo
 

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...

Re: My riddle...From Columbo
 

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.

Re: My riddle...From Columbo
 

You dont need to weigh bag 10, so thats only 45 bars

Re: My riddle...From Columbo
 

...and they only weigh 10 oz. You stack them in a pyramid so you know which layer goes with which bag. No problem.

2 pennies
 

What if you have two pennies, but you are worried that the scale may not be accurate with lots of weight (like over 100oz)?

2 pennies answer
 

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.

Re: 2 pennies answer
 

seems like you could save a little weight by only putting 2 bars from bag 6.

Craig

Re: 2 pennies answer
 

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.

Re: 2 pennies answer
 

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.