A problem by Anshul Gupta
There are 16 boxes each having 3 balls identical in shape and size. 15 of the boxes contains 1 kg balls and one of the 16 boxes contains 2 kg balls. You are given a digital weight measuring machine and marker. What are the minimum number of chances in which box with overweight ball can be spotted out
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1 solution
Number the boxes from 1 to 16 and the balls with same no. as their respective box
Pick 1 ball from first 4 boxes i.e 1 to 4.
2 balls from next 4 boxes i.e. 5 to 8.
3 from next consecutive 4 boxes i.e. 9 to 12.
and no balls from last 4 boxes i.e. 13 to 16
Total expected weight is 4 1+4 2+4*3 = 24 kg If weight comes out to be 25 Kg, Defective ball is from first 4 boxes If weight comes out to be 26 Kg, Defective ball is from next 4 boxes If weight comes out to be 25 Kg, Defective ball is from third group of 4 boxes If weight comes out to same as expected the defective ball is in last group
Then repeat the same procedure with the 4 boxes that are spotted out in first step
You will get the box with overweight ball in 2 chances only