How will u divide 1000 one Rs. Coins in ten bag so that u can give any amount between 1-1000 by just giving the bags without changing the no of coins in each bag.

+1 vote

How will u divide 1000 one Rs. Coins in ten bag so that u can give any amount between 1-1000 by just giving the bags without changing the no of coins in each bag.

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Best answer

By principle of mathematical induction any number can be written as a sum of distinct powers of 2. For proof :(http://faculty.salisbury.edu/~kmshannon/math300/distinctpowers.pdf)

Hence the bags should contain,

1st bag = 1 coin

bag2 = 2 coins

bag3 = 4 coins

bag4 = 8 coins

bag5 = 16 coins

bag6 = 32 coins

bag7 = 64 coins

bag8 = 128 coins

bag9 = 256 coins

bag10 = Remaining 489 coins

...