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Thanks! I am glad you liked my solution. You can credit Charles Naumann.

**cnaumann**- Replies: 19

A friend of mine told me this problem, and I worked out a solution. Then I looked up the solution on this website. I like my solution much better!

The Problem:

You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy).

You have a set scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter).

You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it's heavier or lighter than the rest. How do you do it?

My Solution:

Label the balls 1-12

First Weighing:

Left: 1 2 3 4

Right: 5 6 7 8

Off: 9 10 11 12

Record the heavier side (L, R, or B)

Second Weighing:

Left: 1 2 5 9

Right: 3 4 10 11

Off: 6 7 8 12

Record the heavier side (L, R or B)

Third Weighing:

Left: 3 7 9 10

Right: 1 4 6 12

Off: 2 5 8 11

Record the heavier side (L, R, B)

There are 27 (3^3) possible combination of scale readings. A complete sorted list of the scale reading appears below. Note that only 24 of the 27 readings should be possible given the original problem statement. The algorithm was designed so that if all three scale readings are the same, an error is flagged indicating that the scale is stuck.

BBB Error! There is not a single light or heavy ball (or scale is stuck).

BBL Ball #12 is light

BBR Ball #12 is heavy

BLB Ball #11 is light

BLL Ball #9 is heavy

BLR Ball #10 is light

BRB Ball #11 is heavy

BRL Ball #10 is heavy

BRR Ball #9 is light

LBB Ball #8 is light

LBL Ball #6 is light

LBR Ball #7 is light

LLL Error! Scale is stuck!

LLB Ball #2 is heavy

LLR Ball #1 is heavy

LRB Ball #5 is light

LRL Ball #3 is heavy

LRR Ball #4 is heavy

RBB Ball #8 is heavy

RBL Ball #7 is heavy

RBR Ball #6 is heavy

RLB Ball #5 is heavy

RLL Ball #4 is light

RLR Ball #3 is light

RRB Ball #2 is light

RRL Ball #1 is light

RRR Error! Scale is stuck!

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