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My friend just finished a job interview and was asked the following question that I thought I’d share with you (it’s a somewhat common puzzle):
You are given 8 balls, 7 of which are the same weight and 1 which is heavier than the rest. Using a balance, what is the minimum number of weightings required to determine which ball is the heavier one?
Hint: The answer isn’t 3.
http://firstclassthoughts.co.uk/puzzle/the_8_ball_problem_iq_test.html
The answer is 2.
Divide the 8 balls into 3 groups (3,3,2). Compare the trios. if one trio is heavier, discard the other 5 balls. Compare 2 of the balls in the trio. Whichever is heavier is the right one. If neither ball is heavier, the one you didn’t weigh is the right one.
If the trios weigh the same, then discard both sets of 3 and weigh the 2 remaining balls.
The trick here is to design a test that gets you more data.
If I had started with 2 groups of 4, then I would get 1 data point: which is heavier. Since I picked 3 groups, I actually get 2 data points (out of only 1 test).
the problem can be solved for 9 balls with one heavier!
an old classic: you have 11 eleven equally weighted balls plus a twelfth ball of different weight. determine which ball is different and whether it is heavier or lighter with 3 weighings.