Algorithmic Puzzle [closed]

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How to distribute 1000$ in ten boxes so that any amount of money between $1 and $1000(both inclusive) can be given as some combinations of these boxes.

Please provide any hints on how to approach this.I tried but couldn't make any solution.

Answer 1

Write all the numbers from 1 to 1000 in base-two representation. These numbers require ten bits since 2^10 = 1024. Your boxes are powers of two up to 2^8, and 489 for the last box (2^0 to 2^8 and 489 gives you ten boxes and 2^0 + 2^1 + ... + 2^8 + 489 = 2^9 - 1 + 489 = 511 + 489 = 1000), and the bit representations give you proof that you can write any number of to 1000 as a combination of these boxes (clearly anything up to 511 is okay, for anything greater than 511, subtract 489 and then note that you can write the remainder as a combination of the other 8 boxes since it is guaranteed to be less than or equal to 511).

Answer 2

have you ever did binary to decimal conversion ? Take any number between 1 and 1000 and try converting it into binary. You'll figure out that you are dealing in powers of 2.

Distribute in powers of 2 and then for whatever amount you need, just convert it into binary and pick those boxes for which bit is set to 1.