A real i.q. test?
Suppose that you are given 27 identical balls.
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But one of them is odd in the manner that it is heavy but still identical.
If you are also given a beam balance.
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State and also explain the least number of times you would have to use the balance to determine the odd ball out but remember no probability should be left and no guessing work.
Your answer will determine your I.Q.
The lesser is no. of times the balance used the more is your I.Q.
Remember the answer is not 1.
Hope you'll like this question.
Comments
First weighing:
Split the 27 balls into groups of 9, 9, 9. Put 9 balls on one side, 9 on the other. If one side of the scale goes down, the heavy ball is in that group. If they balance, the heavy ball is in the group you didn't weigh.
Second weighing
Take your heavy group of 9 and split it into 3, 3, 3. Weigh 3 balls against 3 balls. Again, find the heavy group either on the scales if one side goes down, or in the unused group if they balance.
Third and final weighing.
Split the heavy group of 3 into 1, 1, 1. Weigh 1 ball against 1 ball. If one side goes down, that is the heavy ball. If they balance the heavy ball is the one you didn't weigh.
Im not sure if its the least number but it can be done in 3.
group the balls in groups of 9 and weigh put one group on each scale. If they are equal the heavy ball is in the other group, otherwise one groups is heavier but u cant see which it is. with the 9 balls from that group make 3 more groups this time of 3 balls each. same process will tell u which group has heaviest ball. finally with only three balls left put two on the balance and u'll know which one is heaviest.
How much heavier is it? If the odd ball is more than a few grams heavier than the others, you could find it just by picking them up, thus using the balance 0 times.