### Deadly Treasure

A pirate captain presents his prisoner with eight golden coins and a challenge: if the prisoner can identify the single genuine gold doubloon in the bunch, he can keep the coin, and his life. If he chooses one of the seven other counterfeit coins by mistake, he'll have to walk the plank.

The captain leaves the prisoner alone to contemplate this life or death decision. Luckily, there is a double tray balance scale in the room and the prisoner knows that a genuine gold doubloon weighs slightly more than a counterfeit coin. The captain may return any second, so the prisoner only has enough time to load each side of the scale and compare the balance twice. If all the coins look and feel totally identical, how can the prisoner most quickly and confidently identify the genuine article?

Solution: The prisoner places three coins on one side of the scale and three coins on the other for the first measurement. If the scale balances perfectly, he knows that one of the two remaining coins on the table is the genuine gold coin. He measures the two remaining coins and chooses the heavier one. If the first measurement shows that one set of three coins is heavier than the other, the prisoner removes the lighter coins from the scale. He takes the heavier set of three coins, places one on each side of the scale and holds the third in his hand. After the second measurement, he will see which coin on the scale is heavier than the other. If the coins on the scale balance perfectly, he holds the heavier (genuine) coin in his hand!

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## 23 comments

Write a commentAndy Jarvis

Shoot the Captain.

Carlo zorloni

For the first measure, the man puts 3 coins on each plate.

Now we have 2 possibilities:

-the plates weigh equal, so he weighs the 2 coins left and finds the golden one.

-case 2, the 2 plates weigh different, so he takes 1 coin off each plate and switches plate for 2 of the 4 coins (he takes one from rights and puts on the left and viceversa):

Now we have 3 possibilities:

@ the plates are now equal —> the coin he has taken from the lower plate is the golden one.

@ the lower plate is still lower —> the coin that has always been on that plate is the golden one.

@ the plates change position —> the coin he has taken from the lower plate and put on the other one is the golden coins.

Thanks for the challenge <3

P.s. sorry if my english is not perfect

Devon Manning

Load them one at a time on each side until it tips. Once it tips the last coin put on that side will be the real coin

Ka-Lok

1st Balance: Put 3 coins on each side of the scale. 2 sit off to the side.

If they are equal, it’s in the remaining 2 off to the.

Balance again, heavy one is the legit coin.

If they aren’t equal, it must be in the heavier 3. Choose 2 of the 3 and put them on the scale.

One of two results will happen, either they are equal, meaning the one left out is the legit coin, or, one side will be heavier, and again there is your true doubloon!

Waverly

Put 3 coins on each side of the balance. If they are equal weight then weigh the leftover two and the heavier one will be the real gold coin. If one group of 3 coins is heavier then weigh 2 of those 3 coins. If those two are equal then the leftover 3rd coin of the group is the gold coin. If one of the 2 is heavier then that is the gold coin.

Todd Stemple

Samuel Pratt

For the first weighing, put two coins aside and put the other six on the scales, three on each side. If the scale is balanced, then the real coin is one of the other two, and by weighing them against each other you can find whichever is heaviest.

If the first weighing is unbalanced, take whichever 3 coins are heavier and put the rest aside. Put one coin from the three on either end of the scale. If the scales are balanced, the real coin is the one coin left over. If they are unbalanced, the heaviest coin is the real one. :)

Mike

Weight 3 coins vs 3 coins first. If they equal than you know one of the other 2 not weighed is the real coin and you can measure those 2 coins vs each other to see which is heavier. If the 3 coins vs 3 coins are not equal than the side that is heavier has the gold coin. Take 2 of the 3 coins from the heavier side and weight against each other. If they are equal than the 3rd coin is the gold coin. If they are not equal than whichever is heavier is the real gold coin.

Josh Flores

Select from the given coins two groups of three coins each and put them on the opposite cups of the scale. If the first weighing does not yield a balance, the lighter fake is among the three lighter coins. Take any two of them and put them on the opposite cups of the scale. If they weigh the same, it is the third coin in the lighter group that is fake; if they do not weigh the same, the lighter one is the fake.

Thus the problem is solvable in two weighings. It’s not quite clear why the problem has been set up for 8 and not 9 coins. The above solution shows that 1 weighing is sufficient to detect a lighter fake among 3 coins. Splitting 9 coins into three groups and thinking of each as a “big coin”, reduces the problem to the previous one: it takes just one weighing to detect the lighter group. An additional weighing finds the fake coin among the three in the lighter group

Johnny sabino

The real gold coin is the 8.

Because the 8 is a luck number in japan

Jeremiah

Weigh 3 vs 3.

If they are equal, weigh the remaining 2 and the one that weighs more is gold.

If they are not equal, take the 3 from the side that weighs more and weigh 2 of them 1 vs 1. If they are equal, then the one that wasn’t weighed is gold. If they are unequal, then the one that weighs more is gold.

Trung Nguyen

I would load the scale with 3 coins on each side and if they’re balance the real coin would be one of the two that I didn’t balance. That would leave me with my second chance to balance the scale with the two coins. If I scale with three coins on each side and one side is heavier I would take 2 of the 3 coins and measure it and fine the genuine coin this way. If they are the same the 3rd coin I didn’t measure would be the genuine one.

Calvin

You would have to weigh 3 coins against 3 and if they balance, weigh the remaining 2 to identify the heavier. If they don’t, then split the 3 of the heavier side into 1:1 to identify the heavier, and a spare one. If they balance, then it was the spare

Eli

He doesn’t need the scale. He can quickly take 2 coins at a time and try to see which one is obviously lighter.

Jeremiah Dean

You put 3 coins on each side of the scale and if it’s balanced then you put the remaining two on either side of the scale and the heavier one is real.

If it’s unbalanced, you take the heavier 3 coins and set one aside. You weigh the other 2 and the heavier one is real. If they are equal then the third coin is the real one.

Ethan

He should put three doubloons on each side of the scale, and hold the seventh. If they are equal weights, you know the coin he is holding is the real one. If they are not equal weights, the side that weighs more will contain the real one. Take those three coins and place one on each side of the scale, and hold the last. If they are equal, the one he is holding is the real one. If they are not equal, the heavier one is the real one.

Jeremy Libretti-River

He should put 4 coins on each side and then take one off of each side until none are left. One side will be slightly lower than the other in the beginning because it will have the heavier real doubloon. When the side that is lower down raises up to be even with the other side, he knows that the coin he took off of the heavier side is the real doubloon.

Amod Mahadik

First you set 3 coins on each side and put 2 to the side. If the 2 sides are balanced, then those are counterfeit. You then place the two remaining coins, one on each side, on the scale. The heavier one is the real gold coin.

If after the first weighing the scale is not balanced, the coin is one of the three coins on the heavier side. You then take 2/3 coins and balance them out while placing the 3rd to the side. If the coins are equal, the one on the side is real. If they are not equal, the heavier one is the real gold coin.

Eitan touboul

3 and 3 on either side. The side bats heavier has the coin so weigh 2 of them if they are the same the 3rd one out is the coin. If one is heavier that’s the coin. If the initial 3×3 is equal in weight, weigh the next 2. The heavier is the coin.

Anthony

Divide the 8 coins into 3 sets with 3, 3, and 2 in the sets. Put the 3 and 3 on the balance scale. If it balances, the counterfeit coin is in the set of two and another weighing of 1 vs. 1 will show the counterfeit. If the first weighing does not balance, take the lighter set of three and divide it into 3 sets, 1, 1, and 1. Weigh two of these against each other. If they balance the counterfeit is the other one. If they do not balance, the counterfeit is the lighter one. In any case, you only need two uses of the balance scale.

Brian Walsh

Place any 3 on one side of the scale and another 3 on the other. If the scale is equal, the genuine coin is the one left out.

If one side is heavier take the 3 coins from thathe side and do a similar test on that side – 1 coin on each side with the third left off. Whichever side is heavier from that is the real coin, and if the scale is equal again, thenot the one left off is the real coin.

:) Brian

Sam

Riddle solution:

Make two groups of 3, weight each of them

If they are the same then weight the final two of the 8 to find the odd one out,

If they are not equal, take the heavier side and measure two of those, if one of the two is heavier that’s your odd coin out

If those two are equal again, then the third from that group is the heaviest coin

Anthony bromley

You weigh 6 coins. Three on either side. If one side weighs more you weigh that side again. But only two of the coins. If one weighs more that’s the gold. If not it’s the third.

If neither side of the 6 coins weigh more it’s one of the two remaining so weigh both of them.