Weight it
Written on 10:10 am by Vja Students
You have ten boxes, each of which contains nine balls. The balls in one box each weigh 0.9 pounds; the balls in all the other boxes weigh exactly one pound each. You have an accurate scale in front of you, with which you can determine the exact weight, in pounds, of any given set of balls. How can you determine which of the ten boxes contains the lighter balls with only one weighing?
Ans:
Number the boxes 0 through 9. Take zero balls from box 0, one ball from box 1, two balls from box 2, and so on. Weigh all these balls.
Now the required box number = (45-total weight) * 10
Let the boxes be numbered 0,1,...,9
Take the number of balls from each of the boxes equal to the number assigned to the box,
Weigh them together and name the weight 'original',
Then let the total weight of balls (if the weight of each of balls is 1 pound) = (0+1+...+9)*(1 pound) = 45 pound
Now the box number we get = (45-original)*10
Take one ball from 1st Box , 2 balls from 2nd, 3 balls from 3rd and so on....and leave one box as it is , don;t take any ball and weigh all balls together by the scale ..check the fractional part of the total..it will in multiple of 9...if it X.9 ..its first...if it X.8 then 2nd one ...and so on..if its acurate ..then the faulter is last 10th one.