PartialMathematician

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 #1
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I can't do it with 3 uses of saw, but I can do it with 4 uses of the see-saw. 

 

There are 12 people. A,B,C,D,E,F G H I J K, and #. Let's assume # is the odd one. Since we do not know if # is heavier or lighter than the others, this makes it a tad bit harder. 

 

1) Divide the 12 people into two groups. A - F and G - #. We measure one of the groups, 3 on one side and 3 on the other. Let's just say we measure ABC to DEF. If they are equal, that means the odd duck is in the second group. If they are not even, we go to step 2. For our purpose, let's assume Group 2 has the odd one, the #.

 

2) Choose 4 of the 6 from the group and measure them. Let's just say we measure GH and IJ. If they are equal, then the odd duck is in the group of 2. If they are not equal, then the odd duck is inside the group of 4.

 

3) a) If the group has 2 people, in our case K and #, we choose K or # and measure it with one of the normal ones. In our case, let's measure K and G. If they are equal, then the non-measured one (#) is the odd duck, but if they are not equal, then the one that was chosen to be measured with the normal one, in our case K, is the odd duck.

 

3) b) If the group has 4 people, randomly choose 2 people and take them out. Let's make a new scenario, where the group of 4 is I, J, K and #. We randomly choose out K and #. We measure I and J. If they are equal, the odd one is either K or #, which we can find by using step 2 above. If I and J are not equal, then do as above in step 2.

 

4) More of step 2. The 4th step is only needed in some scenarios. 

 

- PM

 

P.S. please send the link to the solution...I want to know a quicker way. wink

 #2
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+2

The same question was asked here on the same website.