Where does the weight go?

Well, I'm back after exams!

A few days back I came across a rather quirky problem which I later remembered to have heard during my childhood. Here is a slightly modified version of that problem.


A man wants to cross a long bridge which can hold only 70 Kg of weight. If you put a little more weight on t, it will collapse. The man weighs 69.9 Kg and he has, say, 10 balls with him each weighing exactly 100 gm. The total weight thus becomes 70.9 Kg. The man can easily cross the bridge taking only one ball with him- but he has to take all the 10 balls with him. (I want to meet the engineer who built the thing: how he determined the exact ultimate stress !! ). It is further given in the problem that he eventually crossed the bridge with all the ten balls. You have to tell how he did it.

No, he didn't throw all the balls across the bridge before he started off. That would be the most foolish thing to do. Let us just assume that it wasn't possible to do that. So, what did he do?

He juggled.

He was a very good juggler. He threw the balls into the air and then caught and threw them again quickly, one at a time, in such a way that at any instant of time he had no more than one ball in his hand. In this way at any given time the total weight the man had on him (including his own) did not exceed 70 Kg. And hence, he crossed the bridge easily, juggling all the way.

यह सॉल्यूशन सुनने के बाद मैंने सोचा, "क्या प्रॉब्लम है, और क्या innovative सॉल्यूशन है!" फिर लगा, "क्या बकवास है!" इस कहानी का end ये नहीं हो सकता।

Instinctively, there has to be a fault in this solution. One cannot take extra weight over the bridge just by juggling. Where does the weight go after all? It has to be taken by the bridge. Can you prove mathematically that the above solution is not viable and that the strength of the bridge has to be at least 70.9 Kg for even the best juggler to pass with ten balls?

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Solution

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