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dpellerin

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You have 10 bags each filled with an unknown number gold coins. You also have a weigh scale. In one of the bags, the gold coins are fake. The other 9 bags each contain real gold coins. The fake coins weigh 10 ounces whereas the real gold coins weigh 12 ounces each. The scale requires a token for each reading and you have only one token with you. So you are allowed to use the weigh scale only ONCE. How do you determine which bag contains the fake coins using only one single weighing?




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Darcy

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Reply with quote  #2 
Duh...   Me thinks the answer to this question is impossible. 

Darcy

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Scott

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Reply with quote  #3 

OK I think I can do this.

 

You’ve got 10 bags. Number then 1 through 10. From bag number 1, take 1 coin, from bag number 2, two coins, bag #3, 3 coins . . . . . and so on up to bag # 10, 10 coins.

Count the coins, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 coins. Now weigh them all together. If all the coins were gold, they would together weigh 660 oz (12 oz per coin x 55 coins).

However, because some are fake and only weigh 10 oz. the total weight will be less than 660 oz. In fact, you will be short 2 oz for every fake coin you have. So if the total weight is short 2 oz, bag #1 must be fake, because you took one coin from bag # 1. If you are short 4 oz, bag # 2 must be fake since you took 2 coins from it, if you are short 6 oz, bag # 3 must be fake., and so on.

 

Scott

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dpellerin

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Reply with quote  #4 
You got it Scott. Well done!
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