you are given 12 spheres and a balance to weigh them, 1 of the 12 spheres weighs less then the other 11, but your only aloud to use the balance 3 times before you lose, how do you find the sphere that weighs less then the others?
we were given the hint that we have to break it into groups of 4, but we still can't find the answer, any help?
we were given the hint that we have to break it into groups of 4, but we still can't find the answer, any help?
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Divide the spheres into 3 groups
Put one group on each side of the balance
- if even, light sphere is in other group - take it
- if uneven - light sphere is in high group - take it
Divide group into 2 pairs and put on scale
- one pair will rise with lighter in it - take that pair
Put one sphere on each pan
- Lighter one will be raised up - take it
3 weighings
Put one group on each side of the balance
- if even, light sphere is in other group - take it
- if uneven - light sphere is in high group - take it
Divide group into 2 pairs and put on scale
- one pair will rise with lighter in it - take that pair
Put one sphere on each pan
- Lighter one will be raised up - take it
3 weighings
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Place two sets of four on either side of the scale. If they balance, then you know that all eight are the same weight, and the remaining 4 have the odd one out. If they don't balance, then the lighter side gives you the four that have the lighter sphere.
Next, take the four with one different sphere, and split them into twos. Choose two. and put them on the balance. If they are the same, then repeat this with the other two, and one will show up lighter.
Next, take the four with one different sphere, and split them into twos. Choose two. and put them on the balance. If they are the same, then repeat this with the other two, and one will show up lighter.