Puzzle

[Neddy]

Here is the situation:

You have 12 cue balls identical in size and color EXCEPT one of the balls does not weigh the same as the other 11. It can be heavier or lighter than the others.

You have one set of balances.

You are allowed to use the balances ony 3 times.

Problem:

Identify which ball is different and tell if the ball is lighter or heavier than the other 11 using the balances only 3 times.

[The_Doctor]

Label the Balls (A-L)

Place A, B,C,D on one side & E,F,G,H on the other.

Case 1: The balance is even (hence odd ball is I,J,K or L).

Place I,J on one side, and K,A

Case 1A: The balance is even.

L is odd (compare with any ball to determine if heavier or lighter)

Case 1B: The I,J was heavier.

Place I on one side and J on the other.

Case 1B1: The balance is even.

K is odd and lighter!

Case 1B2: I is heavier.

I is odd and heavier!

Case 1B3: I is lighter.

J is odd and heavier!

Case 2: The A,B,C,D side was heavier (hence odd ball is A-H - either A-D is heavy or E-H is lighter)

Place on A,B,I on one side and C,D,E on the other side.

Case 2A: The balance is even.

F,G or H is lighter.

Place F on one side and G on the other.

Case 2A1: The balance is even.

H is odd and lighter.

Case 2A2: F is lighter.

F is odd and lighter.

Case 2A3: G is lighter.

G is odd and lighter

Case 2B: A,B,I was heavier.

Either A or B is heavier, or E is lighter.

Place A on one side and B on the other.

Case 2B1: Balance is even.

E is odd and lighter

Case 2B2: A is heavier

A is odd and heavier

Case 2B3: B is heavier

B is odd and heavier

Case 2C: A,B,I, was lighter.

Either C or D is heavier.

Place C on one side and D on the other side.

Case 2C1: C is heavier.

C is odd and heaver.

Case2C2: D is heavier.

D is odd and heavier.

(N.B. case 3 is the reverse of case 2)

[Neddy]

the doctor got it right in record time. Took me working on and off for several days before I gor it.

Good work!!

[Crow Boy]

Here is the situation:

You have 12 cue balls identical in size and color EXCEPT one of the balls does not weigh the same as the other 11. It can be heavier or lighter than the others.

You have one set of balances.

You are allowed to use the balances ony 3 times.

Problem:

Identify which ball is different and tell if the ball is lighter or heavier than the other 11 using the balances only 3 times.

Oh my god - I think I may have started something

the answer came back in record time - I didn't even have time to read the original post before it was solved by the_doctor

CB

[sceadugenga]

Yeah well, I'd have solved it even quicker if I'd seen it first.

http://www.bikwil.com/Vintage06/Billiard-Ball-Puzzle.html

We're all genii with the power of the internet.