HINT FOR PUZZLE-3
Step:1
There may be several ways to approach this problem. One easy way is to start with the number ‘1’and think of the next highest number one can have “as far away” from 1 as possible which will allow us to weigh all integral weights not only up to that number but also up to the sum of the first two weights.
Step:2
Such a number is ‘3’. Now we have ‘1’ and ‘3’ which will allow us to weigh 1,2,3 and 4 with one weighing and nothing beyond. Many people are known to give up this approach at this point thinking that 40 is a long way off and we have already used up 2 out of 4 weights. They hurriedly abandon this approach and try to see some other way and normally get nowhere.
The step beyond:
If you just persist in the same way for one more step, you
will get the answer. ( By now , you must have understood that we have only a “Hobson’s
choice” on the fourth weight as once you choose three weights, the fourth
weight chooses itself.)
