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Here’s another good brain puzzle that’s been asked on job interviews:
You have 8 coins, 1 of which is counterfeit and heavier than the others. You have a balance scale, which you may use twice. How will you figure out which coin is the counterfeit?
Can post your answers to the comments section
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Put 3 coins on each side of the balance.
If the weight is even, then remove the coins and place 1 of the remaining coins on each side. The side that sinks contains the counterfeit coin.
If the weight is uneven, then remove the coins and place 1 of the coins from the side that previosly sank on each side. Which ever side sinks contains the counterfeit coin. If neither side sinks, then the coin not placed on the scale is the counterfeit coin.
weight 3 vs 3.
if they are even, compare the remaining 2 to find the heavier one.
if they are uneven, compare two of the the three that are weigh more.
if they are uneven, then the heavier one is counterfeit.
if they are even, then the 3rd one is counterfeit.
Take six coins and put three on each side of the scale.
If both sides are even, all are real.
If both sides are not even then divide the weight of the lighter 3 coins into 3 to find the weight of one real coin.
Then put two of the heavier three on the scales. If they are both even they are both real and the one left out is the counterfeit. If one is heavier, then it is the counterfeit.
If the two sets of three are even, take the two remaining coins and balance them to see which is the counterfeit. It will be the heavier one.
Place four coins in each balance tray.
Remove the four coins in the lighter side and set aside.
Put two coins from the heavier side in the empty tray.
One side will be heavier.
Remove one coin from each tray. If there is balance, the one removed from the heavier side is the counterfeit. If there is imbalance, obviously the heavier side coin is the counterfeit.
I would take 6 of the coins and divide them into two groups of 3 which I would put on the scale. If these balance then I would simply weight the remaining 2 against each other to identify the heavier.
If at the original weighing I I found one group of 3 was heavier, I would set aside the light group. then from the heavier group I would select 2 and weigh them. If they balance equally then the counterfeit must be the one in my hand and if they dont balance then it is the heavier.
Either way, I would only have used the scale twice and would have my answer.
I should read the answers already given before giving my opinion perhos, i merely repeated what others have already deduced
[...] For a different type of scale balancing puzzle (one that’s been asked on job interviews!), click here. [...]
familiar problem, with correct answers given above
Also, the same question can be stated (as I know it) with 9 coins, the same theory applies
[...] que as restantes. São suficientes pesagens para identificar a moeda contrafeita. Neste post http://www.smart-kit.com/s352/good-math-mind-bender-which-coin-is-the-countefeit/ poderá encontrar, em inglês, um problema semelhante para 8 [...]