a toy company is preparing 1024 gift boes for chrismas party . each box is of same shape ,size,and weight and contains similar type ,shape and weight of pair of skates.
While packing a worker by mistake leaves a cricket ball inside one of the box . At the time of delivery manager came to know about the ball .Suggest way by which manager can find out about the box with a ball in lowest time.
Answers
Answered by
48
According to the Question, there are total of the 1024 gits boxes, which are of the same shape and the same size, and weighs the same.
If the ball is placed in one of the box by mistake, then the box which contains the cricket ball will weighs more in comparison to the other boxes.
Now, Let us consider that the weights of the one box is x grams.
∴ Weight of the 1024 gifts boxes = 1024x grams.
Let the mass of the cricket ball = y grams.
Mass of the One Gift box = x grams.
Mass of the gifts ball which contains the Cricket ball = (x + y) g.
When the manager is ready to deliver the boxes, then he came to know about the cricket ball in the gift. The Quick method, which he can apply in that situation is to weighs the box in comparison to the other.
At first he divides the boxes equally, say one part is 1024/2 = 512 and the others part is also, 512. After dividing, he weighs both the part.
One Part will weighs 512x grams and the other part will weighs (512x + y) grams. It means that one gift box of the second Part which weighs (512x + y) grams which contains the Cricket ball.
Now, In 512 boxes (512x + y grams weights), again he divides them into two parts. First part will be 256 and other part will also be 256. In these part, one part will weighs y grams more than the other part. Thus, the Gift box of this part contained the Cricket ball.
Now, Again we divide 256 into two parts such as first part contains 128 boxes and the other part also contains the same. In this also, one part which weighs y grams more than the other part, contains the Cricket ball.
In 256 boxes, we divide them into two parts namely 128 boxes in each part. Again in this part, one part weighs y grams more than the other part, thus this only contained the box.
In a similar way, he continue to divide. In the last, when he remains with the two gift box, then he weighs both of them, the box which weighs (x+y) grams
contains the Cricket ball.
Hence, the Manager will take out the Cricket ball from that box and transfer the Gifts for the Christmas Party.
Hope it helps.
If the ball is placed in one of the box by mistake, then the box which contains the cricket ball will weighs more in comparison to the other boxes.
Now, Let us consider that the weights of the one box is x grams.
∴ Weight of the 1024 gifts boxes = 1024x grams.
Let the mass of the cricket ball = y grams.
Mass of the One Gift box = x grams.
Mass of the gifts ball which contains the Cricket ball = (x + y) g.
When the manager is ready to deliver the boxes, then he came to know about the cricket ball in the gift. The Quick method, which he can apply in that situation is to weighs the box in comparison to the other.
At first he divides the boxes equally, say one part is 1024/2 = 512 and the others part is also, 512. After dividing, he weighs both the part.
One Part will weighs 512x grams and the other part will weighs (512x + y) grams. It means that one gift box of the second Part which weighs (512x + y) grams which contains the Cricket ball.
Now, In 512 boxes (512x + y grams weights), again he divides them into two parts. First part will be 256 and other part will also be 256. In these part, one part will weighs y grams more than the other part. Thus, the Gift box of this part contained the Cricket ball.
Now, Again we divide 256 into two parts such as first part contains 128 boxes and the other part also contains the same. In this also, one part which weighs y grams more than the other part, contains the Cricket ball.
In 256 boxes, we divide them into two parts namely 128 boxes in each part. Again in this part, one part weighs y grams more than the other part, thus this only contained the box.
In a similar way, he continue to divide. In the last, when he remains with the two gift box, then he weighs both of them, the box which weighs (x+y) grams
contains the Cricket ball.
Hence, the Manager will take out the Cricket ball from that box and transfer the Gifts for the Christmas Party.
Hope it helps.
Answered by
40
The box which has the cricket ball will obviously weigh more than the other boxes. We'll use this fact to find the box.
To find out which box has the extra cricket ball, the delivery manager should divide the boxes into 2 equal sets (of 512 boxes), and whichever weighs more would have the ball.
Next, we divide this set into 2 equal sets (of 256 boxes) and again weigh them, and the heavier set would have the ball.
We will continue with this method till we narrow it down 2 boxes, out of which the heavier one would be the box with the ball.
Problem solved!
To find out which box has the extra cricket ball, the delivery manager should divide the boxes into 2 equal sets (of 512 boxes), and whichever weighs more would have the ball.
Next, we divide this set into 2 equal sets (of 256 boxes) and again weigh them, and the heavier set would have the ball.
We will continue with this method till we narrow it down 2 boxes, out of which the heavier one would be the box with the ball.
Problem solved!
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