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Brain Teaser 4

Eagle 3 · 9 · 1936

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Online Eagle 3

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OK, here's a hard puzzle.

There are 12 boxes that look identical, but one of them is either lighter or heavier than the other 11. Using a balance scale determine which box is the odd one and whether it is lighter or heaver. You only have three weighings.
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Online Robert

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I would do it as follows;

First time on scale 6 on each side, than use the 6 of which one is heavier or lighter
Second time 3 on each side, than use the 3 of which one is heavier or lighter
Third time 1 on each side, is the scale in balance than the one not used is the box you are looking for.
If one of the boxes on the scale is lighter or heavier than that is the one your are looking for.

How am I doing?


Online Eagle 3

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I would do it as follows;

First time on scale 6 on each side, than use the 6 of which one is heavier or lighter
Second time 3 on each side, than use the 3 of which one is heavier or lighter
Third time 1 on each side, is the scale in balance than the one not used is the box you are looking for.
If one of the boxes on the scale is lighter or heavier than that is the one your are looking for.

How am I doing?

No, that doesn't work. Second time the boxes could balance which means that the odd box is one of the 6 that you didn't weigh. What do you do then?
I am sofa king we todd did.


Online Robert

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I thought if you put 6 aside on the scale and e.g. left six are higher (Lighter) or lower (heavier) than the other 6 are out of the game. Continue to do with the remaining six. Ok I am wrong, thought it was easy.


Online Eagle 3

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I thought if you put 6 aside on the scale and e.g. left six are higher (Lighter) or lower (heavier) than the other 6 are out of the game. Continue to do with the remaining six. Ok I am wrong, thought it was easy.
If you weigh 6 and 6, the only thing that you have determined is it the odd box is on the higher side it's lighter and if the odd box is on the lower side it's heavier. Hint: starting with 6 and 6 won't work. Yes, it is not easy. :)
I am sofa king we todd did.


Online Robert

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Ok 3 groups of 4 it is then. Will not reveal correct method so others can have a try. Nice those brain teasers.


Online Eagle 3

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The Solution:

The trick to solving this puzzle is in steps 2 and/or 3, move boxes from one side to the other.

Number the boxes 1 through 12.

Start off with them in 3 groups: [1, 2, 3 and 4], [5, 6, 7 and 8] and [9,10,11 and 12]

Weigh 1, 2, 3 and 4 vs 5, 6, 7 and 8 with 3 possible outcomes:

1.  If they balance then 9,10,11,12 have the odd box, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:

    1a. If 6,7,8 vs 9,10,11 balances, 12 is the odd box. Weigh it against any other box to determine if heavier or lighter.

    1b. If 9,10,11 is heavy then they contain a heavy box. Weigh 9 vs 10, if balanced then 11 is the odd heavy box, else the heavier of 9 or 10 is the odd heavy box.

    1c. If 9,10,11 is light then they contain a light box. Weigh 9 vs 10, if balanced then 11 is the odd light box, else the lighter of 9 or 10 is the odd light box.

2.  If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy box or 1,2,3,4 contains a light box,
    so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:

    2a. If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light box or 7 or 8 is the odd heavy box. Weigh 7 vs 8, if they balance then 4 is the odd light box, or the heaviest of 7 vs 8 is the odd heavy box.

    2b. If 3,6,12 is heavy then either 6 is the odd heavy box or 1 or 2 is the odd light box. Weigh 1 vs 2, if balanced then 6 is the odd heavy box, or the lightest of 1 vs 2 is the odd light box.

    2c. If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other box, if balanced then 5 is the odd heavy box else 3 is the odd light box.

3.  If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy box or 5,6,7,8 contains a light box
    so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:

    3a. If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light box or 3 or 4 is the odd heavy box. Weigh 3 vs 4, if they balance then 8 is the odd light box, or the heaviest of 3 vs 4 is the odd heavy box.

    3b. If 7,2,12 is heavy then either 2 is the odd heavy box or 5 or 6 is the odd light box. Weigh 5 vs 6, if balanced then 2 is the odd heavy box, or the lightest of 5 vs 6 is the odd light box.

    3c. If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other box, if balanced then 1 is the odd heavy box else 7 is the odd light box.


I was given this problem about 50 years ago right after I got my first job as Computer Programmer. I think my boss was testing my analytic ability. It took me about 30 minutes to solve it. I think my boss was amazed that I did it so quickly.
I am sofa king we todd did.


Online dam12641

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Eagle, yeah I knew it was an old one (heard it many times before, so didn't answer), comes around every once in a while.
30 mins 1st time is good going though.   8)

The trick in presenting these old ones is to amend the language so people can't Google the solution (I know you kinda did that with this one {balls to boxes})  Maybe play around with the accompanying verbiage as well. Though it's hard to hide the numbers. But anyone who can understand the numbers enough to search it properly, probably knows the answer already. Damn Google!

Keep it up!  :)


Online Eagle 3

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dam12641, yes it hard to try to amend the puzzles. I'll try harder next time. Speaking of Google, I had a hard time trying to explain the solution to the boxes, so I found a solution after searching Google that was better that I could come up with, so I used it.  ;D
I am sofa king we todd did.