MathDB

In the land of Binary , the unit of currency is called Ben and currency notes are available in denominations

1,2,2^2,2^3,..

Bens. The rules of the Government of Binary stipulate that one can not use more than two notes of any one denomination in any transaction. For example, one can give change for

2

Bens in two ways :

2

one Ben notes or

1

two Ben note. For

5

Ben one can given

1

one Ben and

1

four Ben note or

1

Ben note and

2

two Ben notes. Using

5

one Ben notes or

3

one Ben notes and

1

two Ben notes for a

5

Ben transaction is prohibited. Find the number of ways in which one can give a change

100

Bens following the rules of the Government.

Problem Statement