# U have 16 coins & a balance. 15 of the coins are regular & 1 is a lighter counterfeit coin. Explain how u coul?

You have 16 coins and a balance. Fifteen of the coins are regular, and one is a lighter counterfeit coin. Explain how you could identify the counterfeit coin after the three weightings.

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Put 5 coins on each arm of the balance (=10 with 6 left over)

If the scale balances, the coin is in the 6 left over.

- split those into 3 and 3, weigh them - take the lighter 3

- with the lighter 3, weight one and one, if they are equal the left over one is counterfeit otherwise it’s the lighter of the 2 you weighed.

If the scale doesnt balance, the lighter coin is one of five

- split into 2, 2, 1, weigh the 2s, if the same then the 1 is your counterfeit

- weigh the 2 coins and take the lighter.

mm

take 8 on each side of scale

take lighter side take 3 on one side and 3 on other

if same weigh other 2 if not same weigh 2 of the 3 lighter ones

if same 3rd is lighter

Put eight coins on each side; discard the heavier stack.

Put four coins on either side; discard the heavier stack.

Put two coins on either side; discard the heavier stack.

Then either weigh them or flip a coin.

split it up half and half. of the half that goes up, split that in half. of the half that goes up, split that in half. the one that goes up is the counterfeit.

make it a good day

1. weigh all 16(8/8)..light side 8 remaining

2. weigh remaining 8(4/4) light side 4 remaining

3. weigh remaining 4 (2/2)…light side 2 remaining

ok so you have two coins left..weighed 3x already…

last step, drop the two coins simultaniously..first one to hit the ground is the legitimate coin…the other..is lighter..falls slower..so it is the counterfeit

put 8 coins on each side then put the heavier 8 to one side and put 4 on each side and so on…

I am not sure if you can do it in only three weightings, but here’s is how to do it in four:

Divide them to two group of 8. Weight them, and throw the heavier group away (since that group does not contains the light coin.) Now from that 8, make two group of four and wight them again. Throw the the 4 heavy one away. Now divide them to two group of 2 coin, and weight them for the third time. Choose the lighter group and throw the heavy one away. Now out of those two coins, one is counterfeit. But the only way to tell for sure is to weight each for the FOURTH time. I hope this helps, but I doubt it, since you want the answer in only 3 tries. I thought about it but couldn’t think of anything else. GOOD LUCK.