[QUOTE]Originally posted by magician
[B]

Yes, I meant "guaranty."

 

You said that there were 12 identical, 11 weigh the same amount right? The 12th is heavier or lighter. Trick question? It takes one to find out if it is heaver or lighter, maybe?

 

OK...I think I got it:

You start with 12 blocks so

1 - Leave 2 blocks off the scale and weigh the remaining blocks 5 on one side and 5 on the other
IF a) All 10 blocks balance that leaves the odd block on the ground
Weigh 1 of the blocks that was on the ground with another of the blocks that wasn't. If they balance, the odd block is on the ground - if not, weigh one of those two against another block to eliminate the other block...follow that? - case closed
IF b)One side is heavier than the other:
a) OK...can do it in 4 in the worst case scenario...best I can do. Did do it 3 best case though!! I hate this!!

Mark

 

[QUOTE]Originally posted by skitz
[B]

Ok you put them on the scales.

 

Time to go home, I'll check this thread Monday. Take it easy and have a great weekend everyone!

 

[QUOTE]Originally posted by xviper
[B]
I think it WILL work.

 

[QUOTE]Originally posted by Jeff
[B]You said that there were 12 identical, 11 weigh the same amount right? The 12th is heavier or lighter.

 

Ok heres how to solve this.

Lets number the blocks 1-12

Place 1,2,3,4 on one side 5,6,7,8 on the other.
Either they balance or they don't.
a)If they balance, you weigh 8,10 against 11,12 ( For your second weigh in )
Lets say 8,10 were the light side on the left and 11,12 were the heavy side on the right
Weigh 11 against 12( For the third and final weigh in )
If they are even, then 10 is the light block.
If they are uneven, the heavy side contains the heavy block.

If the 8,10 vs 11,12 measurement was even, then simply weigh the 9 block against a known normal and it will revealed as heavy or light.


b)Now if the first weigh in was uneven we have this situation
Lets say the left side was light.
We have 1,2,3,4 as potential lights and 5,6,7,8 as potential heavies.

Weigh 1,2,6 against 5,3,9 ( weigh in number 2 )
(This is 2 potential lights and a potential heavy against
1 potential heavy, 1 potential light, and 1 normal block)
If this one is even, then we just weigh 7 against 8
If its those are even then 4 is the light one
Otherwise the heavy one between 7 and 8 is the odd/heavy one.

If 1,2,6 vs 5,3,9 was uneven
1) left side light
Either 1 or 2 is a light one, or 5 is a heavy one.
Weigh 1 against 2. (weigh in number 3)
If its even, 5 is the heavy
If its uneven, the light side is the light block.

2) right side light
Either 6 that we moved was a heavy, or 3 that we moved was a light.
So weigh 6 against a standard block and if its heavy, its the heavy.
If its even, 3 is a light.

So thats it. It works with 3 measurements. I understand it even if I can't write it down all that wonderfully.
If you have a right side light situation you just swap the numbers around and it works the same way.

Thanks for helping me pass the last half an hour up here at work.

Can I be an honorary mathematician?

 

Assuming you have to measure all blocks (i.e., no luck involved - 6 .v. 6 remove 1 from each side & they balance, you have your answer), at a minimum 3 measurements are needed to find the ODD block. . . However, 4 measurements MAY be necessary to determine if its lighter or heavier. . .

Here's how:

1st Measurement:
Place four blocks on each side
1,2,3,4, .v. 5,6,7,8

If the blocks balance (the 8 blocks are the same), move on to the final set of 4 blocks. . . Measure the 2 of the final 4 blocks versus 2 from either set of the previous blocks. . .

2nd Measurement:
1,2 .v. 9,10

If they balance, move onto the final 2 blocks. . . Measure 1 of the remaining blocks verus any previous block. .

3rd Measurement:
1 .v. 11

If they don't balance you have your answer, if not. . .

4th Measurement
1 .v. 12

You'll have your answer after 4 measurements. . .


However, if after the 2nd measurement they don't balance remove one block from each side, if they balance you'll have your answer after 3 measurements. . .

3rd Measurement:
1 .v. 9


Note, if after the 1st measurement, the blocks don't balance the scenario is as follows. . .

Remove one blocks from each side. . .

2nd Measurement
1,2,3 .v. 5,6,7

If they balance, you have your answer (LUCK!!!). . . If not, remove another. . .

3rd Measurement
1,2 .v. 5,6

If they balance, you have your answer. . . If not

4th Measurement
1 .v. 5

You'll have your answer. . .

 

Had to take the obvious first. I need to ponder this some more!