You are given 12 seemingly identical metal balls, but one of them weighs slightly more or less than the others. With a balance scale and three weighings only, how can it be determined which is the oddball and whether it is heavier or lighter?

This is one those puzzles that'll likely take a fair amount of time to work out, but the solution (at least the only one I know of) is ingenious and very satisfying to discover. No special math or logic skills required, just perseverance and insight.

### Solution to Twelve Balls puzzle

This one requires a little work and inspiration to solve. I know of only this one solution here. If anyone knows of another, I'd be happy to see it.

Divide the balls into three groups of four each; label these groups

**AAAA, BBBB and CCCC**.

Weigh AAAA_BBBB. The possible results are:

**If they balance:**One of the C's is heavy or light. Therefore:

weigh CCC_AAA (remember, all A's are now known to be standard):**If they balance:**The 4th C is the oddball. Therefore, weigh the 4th C against any other ball.**If the 4th C falls:**The 4th C is heavy.**If the 4th C rises:**The 4th C is light.

**If the CCC side falls:**One of the C's is heavy. (Remember, the A's are known to be standard.) Therefore, weigh C_C:**If they balance:**The other C is heavy.**If one side falls:**The fallen C is heavy.

**If the CCC side rises:**One of the C's is light. Therefore, weigh C_C.**If they balance:**The other C is light.**If one side rises:**The risen C is light.

**If the AAAA side falls:**The oddball is either a heavy A or a light B and the C's are all standard. Therefore, arrange the balls into three new groups like so:**AAAC BBBA CCCB**.**(This re-arrangement step, and the one like it below in step 3, are the key to solving this puzzle.)**Weigh BBBA_CCCB:**If they balance:**The oddball is in AAAC. Therefore, weigh A_A.**If they balance:**The other A in AAAC is heavy.**If one side falls:**The fallen side has the heavy A.

**If the left side (BBBA) falls:**The A in BBBA is heavy or the B in CCCB is light. Therefore, weigh A_C (C is known to be standard).**If they balance:**The B in CCCB is light.**If the A side falls:**A is heavy.**If the C falls:***Not possible.*

**If the right side (CCCB) falls:**The a B in BBBA is light. Therefore, from the BBBA group weigh B_B.**If they balance:**The other B in BBBA is light.**If the left side falls:**The B on the right is light.**If the right side falls:**The B on the left is light.

**If the BBBB side falls:**The oddball is either a heavy B or a light A and the C's are all standard. Therefore, arrange the balls into three new groups like so:**AAAB BBBC CCCA**. Weigh AAAB_CCCA:**If they balance:**The Oddball is in BBBC. Therefore, weigh B_B.**If they balance:**The other B in BBBC is heavy.**If one side falls:**The fallen side has the heavy B.

**If the left side (AAAB) falls:**The B in AAAB is heavy or the A in CCCA is light. Therefore, weigh B_C (C is known to be standard).**If they balance:**The A in CCCA is light.**If the B side falls:**B is heavy.**If the C side falls:**Not possible.

**If the right side (CCCA) falls:**An A in AAAB is light. Therefore, from AAAB weigh A_A.**If they balance:**The other A in AAAB is light.**If the left side falls:**The A on the right is light.**If the right side falls:**The A on the left is light.