# Help with the coin problem!?

You have 12 identical-looking coins but one is actually counterfeit. The coin that is counterfeit is either heavier or lighter that the other eleven coins that all weight the same amount.

The challenge is: Using one balance scale {JUST THREE} times, you must identify the coin that is counterfeit, and whether it is a heavier or lighter coin that the other eleven coins.

How do I solve this problem?

Help please?!

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(1) Put coins 1-4 on the right, 5-8 on the left, and leave 9-12 off.

IF (1) BALANCES: 1-8 are good.

(2) Put coins 1-3 on the right, 9-11 on the left.

IF (2) BALANCES: Coin 12 is bad.

(3) Weigh 12 against 1 to see whether 12 is light or heavy. Done!

IF (2) GOES LEFT SIDE DOWN: The bad coin - 9, 10, or 11 - is heavy.

(3) Put 9 on the right, 10 on the left.

IF (3) BALANCES: Coin 11 is bad (heavy).

IF (3) DOESN’T BALANCE: The heavier coin - 9 or 10 - is bad.

IF (1) GOES LEFT SIDE DOWN: 9-12 are good.

(2) Put coins 1, 5, and 6 on the right; 2, 7, and 8 on the left.

IF (2) BALANCES: Coin 3 or 4 is bad (light).

(3) Put 3 on the left, 4 on the right. The lighter coin - 3 or 4 - is bad.

IF (2) GOES LEFT SIDE DOWN: EITHER 1 is light OR 7 or 8 is heavy.

(3) Put 7 on the left, 8 on the right.

IF (3) BALANCES: Coin 1 is bad (light).

IF (3) DOESN’T BALANCE: The heavier coin - 7 or 8 - is bad.

IF (2) GOES RIGHT SIDE DOWN: follow similar procedure with 2, 5, and 6.

IF (1) GOES RIGHT SIDE DOWN: follow the same procedure, reversing light & heavy.

this is only applicable if we know that counterfeit is heavier or lighter.

we cannot determine if we don’t know is it heavier or lighter.

divide the coin into 3

A B C

x x x x || x x x x || x x x x

scale the A and B.

if either side is heavier then we know the counterfeit coin is on A or B. if not automatically it is C

so we have reduce the possibilities into four coins

divided into two groups

A B

x x || x x

scale the coins and determine which site is heavier or lighter

then continue with scaling the two coins possibilities. and you will get the answer.