Puzzle 11 | ( 1000 Coins and 10 Bags )

A dealer has 1000 coins and 10 bags. He has to divide the coins over the ten bags so that he can make any number of coins simply by handing over a few bags. How must divide his money into the ten bags? 

Find the ages of daughters

Solution:

The idea of filling coins in the powers of 2 can be get from the condition that was given the question that each bag can be given or not given: we are not allowed to open the bag and give some coins. So we can represent each bag as each place value which takes either the value of 0 or 1.

Example:

If we have to give 7 coins then it is nothing but 0000000111 the last 3 digits of 1 represent that those 3 bags whose place values are 1,2,4 are to be given to give 7 coins. 
Remember that each bag should be either given or not given, which means there are only 2 choices to us, which is similar to the numbers in base 2 where each digit has only 2 values either 1 or 0.
We can fill coins in the 10 bags in increasing order of 2^n where n varies from 0 – 8, filling the last bag with all remaining coins as follows: 

1 = 2^0 = 1 
2 = 2^1 = 2 
3 = 2^2 = 4 
4 = 2^3 = 8 
5 = 2^4 = 16 
6 = 2^5 = 32 
7 = 2^6 = 64 
8 = 2^7 = 128 
9 = 2^8 = 256 
10 = remaining coins = 489 

Now, the dealer can make any number of coins just by handing over the bags. 

As, 
number of coins needed = some bag 1 + some bag 2 + ….. + some bag n 
example: 
519 coins = bag 2 + bag 4 + bag 8 + bag 16 + bag 489 

Factorization algorithms other than powers of 2 are costly on computer systems. Please share any other information. Any person working on cryptography can share more details.