Weighing 10 Bags Puzzle

posted by saurabh
- October 15 2014 11:19:18 AM

You have 10 bags full of coins, in each bag are 1,000 coins.

But one bag is full of forgeries, and you can't remember which one.

But you do know that a genuine coins weigh 1 gram, but forgeries weigh 1.1 grams.

To hide the fact that you can't remember which bag contains forgeries, you plan to go just once to the central weighing machine to get ONE ACCURATE weight.

How can you identify the bag with the forgeries with just one weighing?

And what if you didn't know how many bags contain forgeries?

But one bag is full of forgeries, and you can't remember which one.

But you do know that a genuine coins weigh 1 gram, but forgeries weigh 1.1 grams.

To hide the fact that you can't remember which bag contains forgeries, you plan to go just once to the central weighing machine to get ONE ACCURATE weight.

How can you identify the bag with the forgeries with just one weighing?

And what if you didn't know how many bags contain forgeries?

Reply by saurabh
- October 15 2014 11:20:33 AM

you can pick different amount of coins from each of the bags

Reply by Braintraining
- November 06 2014 05:06:42 AM

Easy, you pick a coin from each of the bags, you must remeber which coin belongs to which bag, you take ten coins and weigh them one by one.

Reply by Braintraining
- November 06 2014 05:07:04 AM

Please do tell me if I am right or not? :)

Reply by insertcleverphrase
- March 11 2015 06:03:22 AM

[hide]since the forgeries weigh 10% more than the normal coins, there are actually a number of solutions to the first part of this riddle, while i can only thin of one to the second part.

The easiest i can think of for the first part is to take 1 coin from the first bag, 2 coins from the second bag, etc. or 10! coins (55).

if you weigh these coins they will weigh 55.1 grams if it was the first bag, 55.2 grams if it was the second bag, etc.

For the second part, where you don't know how many bags contain forgeries, if you chose numbers of coins from each bag so that no combination of previous amounts could add up to the others, which ends up as squares of two, but starting with 1: 1,2,4,8,16,32,64,128,256,512 (lucky we don't have 11 bags), then weigh this total, the resulting weight will be unique, and will tell you how many, and which bags contain forgeries.

if no bags contain forgeries, it will weigh 1023 grams, if only bag 1 contains forgeries, it will weigh 1023.1 grams, if bags 1, 3, 5, 7, and 9 contain forgeries it will weigh 1023+32.1 grams, and so on. [/hide]

The easiest i can think of for the first part is to take 1 coin from the first bag, 2 coins from the second bag, etc. or 10! coins (55).

if you weigh these coins they will weigh 55.1 grams if it was the first bag, 55.2 grams if it was the second bag, etc.

For the second part, where you don't know how many bags contain forgeries, if you chose numbers of coins from each bag so that no combination of previous amounts could add up to the others, which ends up as squares of two, but starting with 1: 1,2,4,8,16,32,64,128,256,512 (lucky we don't have 11 bags), then weigh this total, the resulting weight will be unique, and will tell you how many, and which bags contain forgeries.

if no bags contain forgeries, it will weigh 1023 grams, if only bag 1 contains forgeries, it will weigh 1023.1 grams, if bags 1, 3, 5, 7, and 9 contain forgeries it will weigh 1023+32.1 grams, and so on. [/hide]

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