Find a box of defective balls puzzle (Logical Interview question)

Question: box of defective balls puzzle or logical interview question

  1. You are given 10 boxes containing balls.
  2. The 9 boxes contains the balls, each ball weighing 10 gm
  3. The 1 box (defective box) contains the balls, each ball weighing 9 gm.
  4. You are given electronic weighing machine and you can use the weighing machine only once.
  5. Find out the defective box among 10 boxes (box containing balls of 9 gm weigh)

Solution: box of defective balls puzzle or logical interview question

  1. Suppose boxes are labelled from 1 to 10.
  2. Take 1 balls from box 1, 2 balls from box 2, 3 balls from box 3 and so on. At last take 10 balls from box 10.
    • Sum(n) = n(n+1) / 2
    • Total numbers of balls  = (10 * 11)/ 2 = 55
  3. If all 10 boxes had contained 10 gm balls, Total weight would be:
    • Total weight = 55 * 10 gm = 550 gm
  4. But, We have a box which contains 9 gm balls.
    • We will not get sum of 550.
    • Our sum will be reduced.
      • Depending upon, how many defective balls ,we have picked (Step 2).
  5. If Sum, we get due to defective box is 549, which is 1 less than possible sum of 550.
    • It mean we have 1 defective ball
    • We have picked 1 ball from box number 1.
    • Then box number 1 is defective box.
  6. If Sum is 548, which is 2 less than possible sum of 550.
    • It mean we have 2 defective balls
    • We have picked 2 ball from box number 2
    • Then box number 2 is defective box.
  7. Similarly, if Sum is 540, which is 10 less than possible sum of 550.
    • We have picked 10 ball from box number 10
    • Then box number 10 is defective box.
  8. We can identified the defective box among 10 boxes.
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