Question

Put 63 one rupee notes in 6 envelopes so that any integral sum from Rs 1 to Rs 63 rupees can be paid without opening the envelopes.

Answer 1

The envelop should be 1 ,2 ,4 ,8 ,16 and 32 so that the sum of these number would be 32
example
For 43: 32 + 8 + 2 + 1
similarly 
For 63 : 32 + 16 + 8 + 4 + 2 + 1
and for 14 ; 8 + 4 + 2

Answer 2

Solution :-

Total envelopes = 6

The number of one rupee notes should be 1, 2, 4, 8, 16 and 32 in six envelopes.

It means in the first envelope, there is 1 one rupee note.

In the second envelope, there is 2 one rupee notes.

In the third envelope, there is 4 one rupee notes.

In the fourth envelope, there is 8 one rupee notes.

In the fifth envelope, there is 16 one rupee notes.

In the sixth envelope, there is 32 one rupee notes.

By this way, any integral sum from Rs.1 to Rs. 63 can be paid without opening the envelope.

Example :

For Rs. 39 = 32 + 4 + 2+ 1

For Rs. 57 = 32 + 16 + 8 + 1

For Rs. 19 = 16 + 2 + 1