There were three brothers Albert, Bertrand and Charles.

Albert lent to Bertrand and Charles as many books as they had initially.

After some time Bertrand gave as many books to Albert and Charles as many as they now have.

After sometime Charles did the same thing.

At the end each one of them had 24 books.

Find the books each orginally had.

I got the same solution as Tom, but in a simpler way. Taking A, B and C as the number of books that Albert, Bertrand and Charles have resp. and starting from the final step...

Last position:
A=24, B=24, C=24

To get to the last point Charles doubled the number of books that both Albert and Bertrand had, therefore after the second exchange...

A=12 (=24/2), B=12 (=24/2), C=48 (=24+12+12)

In the second exchange Bertrand doubled the number of books held by Albert and Charles, therefore after the first exchange...

A=6 (=12/2), B=42 (=12+6+24), C=24 (=48/2)

In the first exchange Albert doubled the number of books held by Bertrand and Charles, therefore the start position was...

Start position:
A=39 (=6+21+12), B=21 (=42/2), C=12 (=24/2)

Posted by fwaff on 2003-02-03 00:59:36