Can you find the sac with counterfeit gold coins?
In a room with 10 sacs of gold coins, there is 1 with countterfeit ones, the only diference is that, the real ones weight 10 grams, the counterfeit weight 1 gram more or less, 9 or 11 grams. You have a electronic scale that you can use only once, This is not a trick question, there is a solution, Can you tell me?
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If sacs are numbered 1 to 10 and coins are put in the pan of the scale (1 coin from sac #1, 2 from sac #2, and so on, …, 10 from sac #10) and weighed then
if they weigh (550 + n)g or (550 — n)g, the sac #n contains counterfeit coins.
you can find it by computing the density… various substances have various densities…
Take one coin from the first sack, two coins from the second sack, three from the third sack, etc. for a total of 55 coins.
Weight them. If none were couterfeit they should weigh 550g. The difference in the actual weight will tell you which sack is the counterfeits.
I.e. if you got a weight of 558g then their must be 8 counterfeit coins on the scale and you took those eight from the 8th sack and they all weigh 1 gram extra.
If on the other hand you got a number under 550g the counterfeit coins would only be 9 grams.
I know this is the wrong answer, but I personally would skip the scale, take a coin from each sack (marking which coin came from which) and go to a coin specialist and have them decide. There are chemical tests that can be done.
Or scrap the sackful that is imprinted "In Dog We Trust"
count the coins in all the bags
the one with a different number of coins is the one with the counterfeit coins
You take a coin from each sack and put it on the scale one at a time, and the one that weighs more or less than 10 grams is fake… so you remember which bag it came from?