Life is a Test: A Series of Pony Logic Puzzles

by Brony_of_Brody

The Answer 12

If you knew if the twelfth coin was lighter or heavier, this would be easier. But you don't, so...

Number each coin 1-12. Split the coins into groups of four numerically, then take group 1234 and weigh it against 5678.

IF FIRST WEIGHING BALANCES:

1.1 Now you know one of the coins you didn't weigh is the one you're looking for. Remove all coins except coin 8, then weigh 9 and 10 against 11 and 8.

IF THEY BALANCE AGAIN:

1.1.1 Great! You've weighed 11 coins and they're all equal, ergo the twelfth un-weighed coin is the one you seek.

IF THEY ARE NOT BALANCED:

1.1.2 In the event side 9 and 10 is lighter than 11 and 8, either 11 is heavier than the others, or either 9 or 10 is lighter than the others. So weigh 9 against 10. If they balance, it means 11 is heavier. If not, you know that either 9 or 10 is lighter than the others, so the lighter coin must be the different one.

1.1.3 But if side 9 and 10 is heavier than side 11 and 8, same logic applies. Either 11 is lighter or 9 or 10 is heavier. Weigh 9 against 10. If they balance, 11's the one. If not, the heavier coin is the different one.

IF FIRST WEIGHING IS NOT BALANCED:

1.2 In the event side 1234 is lighter than 5678, it means either 1234 is lighter or 5678 is heavier. So take coin 9 and weigh 1, 2 and 5 against 3, 6 and 9.

1.2.1 If they balance, either 4 is light or 7 or 8 is heavy. You then simply weigh 7 and 8, and if they balance, 4 is light. If not, the heavier coin is the one.

1.2.2. If (when we weigh 1,2, and 5 against 3,6 and 9) the right side is heavier, then either 6 is heavy or 1 is light or 2 is light. By weighing 1 against 2 the solution is obtained.

1.2.3. If (when we weigh 1,2, and 5 against 3, 6 and 9) the right side is lighter, then either 3 is light or 5 is heavy. By weighing 3 against a good coin the solution is easily arrived at.

1.3 If (at the first weighing) coins 1,2,3,4 are heavier than coins 5,6,7,8 then repeat the previous steps 1.2 through 1.2.3 but switch the numbers of coins 1,2,3,4 with 5,6,7,8.

Comments

[Andy Ray]

Huh, well... The trickiest part was when the 8 being weighed were unbalanced, anyway... I might be right, though.

Moving sides for coins? O-o-oh !..