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You have 10 boxes with a thousand coins...

K

Kntx

Platinum Member
Here's a little brain teaser for all who are interested...

You have 10 boxes with 1000 coins in each box. In 9 of the boxes each coin weighs 10 grams. In 1 of the boxes each coin weighs 11 grams. Using a balance type scale and taking only one reading, how could you find out which box contains the 11 gram coins?

You can move coins between boxes and do whatever you want, but may only use the scale once.

Have fun.
 
technically you don't even need to take a reading on the balance. The 1000 gram difference in wieght would be pretty apparent as you put them on the scale.

m00se
 
lift a couple, the heavier one is the one with the bigger coins. 1000grams would make a large differenec in the weight.
 
you take one coin from the first box, two from the 2nd, 3from the third, 4 from the 4th, 5 from the 5th, 6 from the 6th, 7from the 7th, 8from the 8th, 9from the 9th, and 10 from the 10th.

combine and weigh once.

since 9 out of the 10 boxes contained 10g coins, those would have a weight divisble by 10.

therefore if the last digit of the weight is 1, the 11g was in the 1st box.
therefore if the last digit of the weight is 2, the 11g was in the 2nd box.
therefore if the last digit of the weight is 3, the 11g was in the 3rd box.
therefore if the last digit of the weight is 4, the 11g was in the 4th box.
therefore if the last digit of the weight is 5, the 11g was in the 5th box.
therefore if the last digit of the weight is 6, the 11g was in the 6th box.
therefore if the last digit of the weight is 7, the 11g was in the 7th box.
therefore if the last digit of the weight is 8, the 11g was in the 8th box.
therefore if the last digit of the weight is 9, the 11g was in the 9th box.
therefore if the last digit of the weight is 0, the 11g was in the 10th box.



 


<< Here's a little brain teaser for all who are interested...

You have 10 boxes with 1000 coins in each box. In 9 of the boxes each coin weighs 10 grams. In 1 of the boxes each coin weighs 11 grams. Using a balance type scale and taking only one reading, how could you find out which box contains the 11 gram coins?

You can move coins between boxes and do whatever you want, but may only use the scale once.

Have fun. >>




Drop the coin from each box into a graduated cylinder filled with known amount of water and find out the volume of a coin from each box. I'm guessing the 11gram coins have different volume.
 
With a balance scale you would have to pick a box, take 55 coins and place them on the other side of the balance. If that is heavier then the first set of coins you found the 11g coins. If it is lighter continue adding coins until you achieve a balance the number of coins in excess of 55 is the number of the box which contains the heavy coins.
 
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