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Answer to "A weighty problem"

First  weighing:
Divide the 27 balls into 3 groups of 9 balls each.
Set one group aside and weigh the other 2 groups against each other (ie one group in each pan of the scale).
From the way the scale tilts you can determine which of the two groups (of 9 balls each) contains the heavier ball. If the two groups balance then the odd ball is in the group you set aside.

Second  weighing:
Take the errant group (of 9 balls) and divide it into 3 groups of 3 balls each.
Again set one group aside and weigh the other 2 groups against each other.
From the way the scale tilts you can determine which of the two groups (of 3 balls each) contains the heavier ball. If the two groups balance then the odd ball is in the group you set aside.

Third  weighing:
Take the errant group (of 3 balls) and set one ball aside.  Weigh the other two balls against each other.
From the way the scale tilts you can determine which is the heavier ball.
If the two balls balance then the heavier ball is the one you set aside.

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