Ball in the box

Logic Level 3

There are 10 boxes, of 10 balls in each of the box. Each ball weigh $10\text{ g}$ . Now for instance, Any one of the box is replaced with another box, of each 10 balls, where each ball weigh $9\text{ g}$ instead . You have one electronic machine.

Find out how many number of trails you need to find which box contains $9\text{ g}$ balls.

Clarifications :

Taking a box is counted as a trail (eg. taking 2 boxes means 2 trails)
Taking balls from any boxes is counted as a trail (eg. taking 1 ball from first box, 5 balls from last box means 1 trail only)

The answer is 1.

1 solution

Viki Zeta
Jul 22, 2016

Let boxes with 9g and 10g totally be represented as $Box_1, Box_2, \ldots, Box_10$ Now, take 1 ball from $Box_1$ , 2 balls from $Box_2$ , and similarly until $Box_10$ . Now sum the weights of all the balls, let it be $x$

Now, assuming all the balls as 10g, the total weight would be, $\text{Total no of balls }\times 10g = (1+2+3+\ldots+10) \times 10 = 50 * 10 = 500g$ .

Now, weight of $x$ is lesser than 500g, as weight of x have one 9g in it. So, now let's subtract 500 and $x$ . Compare the result, if the result is lesser than 1, then the box from which one ball is taken have 9g (ie, $Box_1$ ), if the result is lesser than 2, then the box from which two ball is taken have 9g (ie, $Box_2$ ), etc...

So you can easily find it in a trail

Ball in the box

The answer is 1.

1 solution

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