A Box of Defective Balls (1 Box in total of 10 boxes)

You have 10 boxes of balls (each ball weighing exactly10 gm) with one box with defective balls (each one of the defective balls weigh 9 gm). You are given an electronic weighing machine and only one chance at it. How will find out which box has the defective balls?


Mark the boxes as box1,box2,box3………box10
then from 1st box we have to take 1 ball,from 2nd box 2 ball……….from 10th box we kept 10 balls. and weight the total ball….

so if total nos ball is :n(n+1)/2 (n= total nos of box that is 10)=55
if all the ball is 10 gm.then total weight will be=550gm.
suppose total weight is 546gm.
so the difference is(550-546=4gm).
then the d defective ball is in box no:4.
similarly we can try for all possible box difference gives us the box number which contains the defective balls

Gold Bar For 7 Days of Work

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?


Day 1: Give worker 1 bar
Day 2: Take back 1 bar and give 2 piece bar
Day 3: Give 1 bar [Making 2 + 1 = 3]
Day 4: Take back 1 & 2 piece bar and give 4 piece bar
Day 5: Give 1 piece bar [Making 4 + 1 = 5]
Day 6: Take back 1 piece and give 2 piece
[Making 5 - 1 + 2 = 6]
Day 7: Give 1 piece bar