12 Balls Puzzle Answer: Find the Odd Ball in 3 Weighings [Solved]

The 12 balls puzzle answer: weigh 4 balls against 4 balls first, use the known good balls in the second weighing, and finish in the third weighing. You can name the odd ball and say whether it is heavier or lighter, every time, with no luck involved.

The 12 balls puzzle answer is simple to state and hard to find under pressure. You have 12 balls that look identical. Eleven weigh exactly the same. One ball is different, but you do not know whether it is heavier or lighter. With a two pan balance scale and only 3 weighings, find the odd ball and say whether it is heavier or lighter. A plan that finds the ball but cannot say heavier or lighter is only half an answer.

The Puzzle, Stated Exactly

Number the balls 1 to 12. The scale has no numbers. It only tells you three things: the left pan goes down, the right pan goes down, or the pans balance. You have no known weights, only the balls. You get 3 weighings, and each later weighing can depend on earlier results.

This is the classic 12 ball weighing problem, listed in interview brain teaser collections and reported in candidate shared interview reports for quantitative trading roles, where 12 marbles, one of a different weight, must be solved in at most 3 weighings. The solution below is original.

How the 12 Balls Puzzle Answer Works

Count the possibilities first. There are 12 balls, and each one could be heavier or lighter, giving 24 possibilities. Each weighing has 3 outcomes, so 3 weighings give 27 outcome patterns. Since 27 is just above 24, a perfect plan is possible, but only just. Every weighing must split the remaining possibilities into three useful groups, and every weighing must use what earlier weighings already proved.

That count explains why the obvious first move fails. Weighing 6 against 6 leaves 6 suspects on one side and no clean finish in 2 more weighings. Weighing 1 against 1 wastes a full weighing on 2 balls. The winning first move is 4 against 4, leaving 4 balls off the scale and creating known good balls in one outcome.

Step 1: Weigh 4 Against 4 in the 12 Balls Puzzle Answer

Put balls 1, 2, 3 and 4 on the left pan, and balls 5, 6, 7 and 8 on the right pan. Leave balls 9, 10, 11 and 12 off the scale. If the pans balance, the odd ball is off the scale, so balls 1 to 8 are all normal and the odd ball is 9, 10, 11 or 12. If the pans tip, the odd ball is on the scale, and balls 9 to 12 are all normal. Remember this rule: the side that goes down holds either a heavy ball, or, on the other side, a light ball.

If the First Weighing Balances

This is the easy case. Balls 1 to 8 are known good. For the second weighing, put balls 9, 10 and 11 on the left pan and three known good balls, say 1, 2 and 3, on the right pan. If the pans balance, ball 12 is the odd ball. Weigh it against a known good ball in the third weighing, and the direction tells you heavier or lighter.

If balls 9, 10 and 11 go down, the odd ball is heavy and it is one of those three. Weigh ball 9 against ball 10. The heavier one wins, and a balance means ball 11 is the odd heavy ball. If they go up, the same logic works in reverse, with the lighter winning and a balance meaning ball 11 is light.

If the First Weighing Tips

Now take the harder case. Suppose the left pan goes down. That means one of balls 1, 2, 3 or 4 is heavy, or one of balls 5, 6, 7 or 8 is light. Balls 9 to 12 are known good. If your first weighing tips the other way, just swap heavy and light in everything that follows. The structure is identical.

The Second Weighing

For the second weighing, put balls 1, 2 and 5 on the left pan, and balls 3, 6 and 9 on the right pan. Ball 9 is a known good ball, added only to make three balls per pan. Balls 4, 7 and 8 stay off the scale. This weighing looks strange on purpose. It moves some suspects to the other pan and leaves some off, so each outcome points to a small group.

Second weighing result	Suspects left
Left pan goes down again	Ball 1 heavy, ball 2 heavy, or ball 6 light
Right pan goes down	Ball 3 heavy, or ball 5 light
Pans balance	Ball 4 heavy, ball 7 light, or ball 8 light

Check the table. Balls 1 and 2 are heavy candidates on the left in both weighings, so a second left tip keeps them alive. Ball 6 is a light candidate on the right in the second weighing, and a light ball on the right also tips the left pan down. Ball 3 is a heavy candidate moved to the right, and ball 5 is a light candidate moved to the left, so both flip the tip to the right. Balls 4, 7 and 8 never touch the second scale, so a balance leaves exactly those three.

Finishing Each Branch

Each group now fits in one weighing. Left tip again: weigh ball 1 against ball 2. The heavier one wins, and a balance means ball 6 is light. Right tip: weigh ball 3 against known good ball 9. If ball 3 goes down, it is heavy, and a balance means ball 5 is light. Balance: weigh ball 7 against ball 8. The lighter one wins, and a balance means ball 4 is heavy. Every branch ends in 3 weighings, with the ball named and its direction stated.

Two Worked Traces to Test Yourself

Do not trust the table until you trace a ball through it. Suppose ball 7 is light. At the start, ball 7 sits on the right pan, so the left pan goes down. Then ball 7 stays off the scale for the second weighing, so the pans balance. For the finish, ball 7 against ball 8 tips the right pan up, so ball 7 is lighter. The plan finds it.

Next, suppose ball 3 is heavy. First weighing: left pan down. Second weighing: ball 3 moves right, so the right pan goes down. Third weighing: ball 3 against known good ball 9 goes down, so ball 3 is heavy. Try a third trace of your own choice.

The Traps That Catch Good Candidates

One trap is starting with 6 against 6, which throws away the chance to create known good balls early. Another is forgetting those known good balls and weighing suspects against suspects, when a known good ball lets you test one suspect cleanly, as with ball 3 against ball 9. A third mistake is stopping without saying heavier or lighter. Finally, never assume the odd ball is heavier, because the question never says that.

What the Interviewer Is Testing in the 12 Balls Puzzle Answer

This puzzle tests whether you count possibilities before you start, whether you use information fully, and whether you can hold a branching plan without losing a case. A candidate who notes 24 possibilities against 27 outcome patterns shows why 3 weighings can work and why there is no room to waste one. It also tests communication: state the answer, state the first weighing, walk the cases in order, and trace a sample ball on request.

Try It Yourself Before the Interview

To prepare, write the numbers 1 to 12 on slips of paper, pick one in secret, mark it heavy or light, and run the plan. Spend most of your practice on the tipped case, where the second weighing of 1, 2 and 5 against 3, 6 and 9 does the hard work.

Can you do it in 2 weighings?

No. Two weighings give only 9 outcome patterns, and there are 24 possibilities to separate. Three weighings give 27 patterns, which is just enough.

Does the plan work if the odd ball is lighter?

Yes. Every branch names a direction. The light candidates in the tipped case are balls 5, 6, 7 and 8, and the third weighing settles each one.

One More Puzzle to Try

If you liked the counting logic here, try the 100 Doors Puzzle Answer: 10 Open Doors, where a small case plus a pairing argument does the heavy lifting. Or test your step by step reasoning with the Ants Triangle Puzzle Answer: 1 in 4, which rewards the same kind of structural insight. The question for this post is the classic 12 ball weighing problem, as listed in interview brain teaser collections and reported in candidate shared interview reports for quantitative trading roles. The solution and all text above are original.