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- anonymous

You have 26 weights, one of which is lighter than the other 25. How would you determine the light weight in three separate weighings on a balance scale?

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- anonymous

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- anonymous

if anyone can help me out with this problem by tonight that would be great, I would really appreciate it!

- amistre64

I dont know an answer right off hand, but what are your thoughts about it so far?

- amistre64

3 seperate weighings means that we would have to have 3 seperate groups to weigh in my thinking.. and you only have a 1 in 26 chance of picking the right one.

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- amistre64

26/2 = 13 so pick the side that is lighter and you have 13 to choose from...

- amistre64

split that up to 6 and 7; the heavier side is off by the lighter weight
choose the 7 to work with

- amistre64

or; from the 13 choose one weight not to weigh, if they come out equal, you have the lighter one. If not, choose the lighter side again?

- amistre64

I can do it in four weighings :)

- radar

What about dividing the weights into three piles, two piles with 9 and one pile with 8
Place the two piles of 9 on the balance scale. Their is only two conditions that can take place 1. The scales are balanced which means the lighter one is in the pile of 8. or 2. The scales are unbalanced. Lets go with situation 2 and remove the lighter (higher side of scale) Now divided these 9 into three piles of three. This would be the second weighing place two piles on three on each side of the scale. If balanced then the lighter weight is in the remaing pile (as before the two conditions are a balance or an unbalance. If they are unbalanced then remove the lighter side and using the third measurement place one on each scale and locate the lighter one. If it were balanced on the second weighing then get the remaining three and place one on each side of the scale and locate the lighter with the third weighing.
Now for the earlier case no 1 after the first weighing. Take the eight from that third pile and divide them into a group of three, another group of three, and a group of two. For the second weighing place the two groups of three on the balance scale. This second weighing will either be balanced telling you the lighter weight is in the group of 2, if this is the case, then weigh those two for your third weighing and select the lighter, The case was unbalanced for the second weighing, remove the three from the lighter side, and place two of them on the scales (one each side) and select the lighter one from this final or third weighing.

- amistre64

got it; i think :)
split the load 9 - 9 - 8
1) weigh 9 - 9 and if equal; L is in 8.
split 8 to 3 - 3 - 2
weigh 3 - 3, if equal then L is in 2 and weigh 1 - 1
if 3 - 3 is not balanced, pick lighter side.
weigh 1 - 1; if equal, L is on the ground, if not equal L is lighter one.
2) weigh 9 - 9 and not balanced; L is in lighter side
split to 3 - 3 - 3
weigh 3 - 3 and if balanced L is in 3 on ground; if not balanced L is in lighter side with (3) either way you have 3 to weigh.
weigh 1-1 if equal L is on ground; if not equal, L is lighter side.
All done in 3 weighings :)

- amistre64

It took me awhile, but yeah....i agree with radar :)

- radar

amistre64 as usual you did a very coherent and numerical approach. I was trying to use logic, we both arrived at the same conclusion.

- anonymous

thank you both for your great help!

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