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.
Asked
Active
Viewed 249 times
-4
-
4big hint: powers of 2 – Lior Kogan Jul 05 '13 at 05:13
-
3This question appears to be off-topic because it is about not programming related. – Lior Kogan Jul 05 '13 at 05:18
-
@Lior Kogan:so can you provide any links where i can post such questions?? – user122345656 Jul 05 '13 at 05:20
-
This is a puzzle rather a typical brain teaser where in little bit of computer fundamental(Base 2 conversion) would make you come to the solution. – roger_that Jul 05 '13 at 05:21
-
@user122345656: Please provide a clear question, as it is the question is very confusing.What does combinations mean? – Aravind Jul 05 '13 at 05:22
-
@Jason: the largest can be 489 – Lior Kogan Jul 05 '13 at 05:25
-
@Aravind: Combination means does any boxes exists that sum up to a given amount. Say one want $3 so combination of boxes whose amount sum to $3(like :$1 and $2) will work. – user122345656 Jul 05 '13 at 05:35
-
@Jason:Yes amount is $1000 – user122345656 Jul 05 '13 at 05:37
2 Answers
3
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.
roger_that
- 9,493
- 18
- 66
- 102
-
What do you mean by "you are dealing in powers of 2"?Could you elaborate a bit? – Aravind Jul 05 '13 at 05:34
-
How do you convert a decimal into binary? You have a kind of GP series with common ratio = 2. Like if you need to convert 15(let say the amount) then you will have : **.....,16, 8, 4, 2, 1 ** something of this sort and for 15, you need last four numbers (8+4+2+1) means these bits are set to 1 gives you 1111 as 15. Now, in terms of puzzle, put the amount in boxes in forms of powers of 2 and then for 15, convert it to binary, find the set bit, and pick boxes for those numbers. – roger_that Jul 05 '13 at 06:11
-
-
@VaibhavShukla: Thanks, I din't understand the question, once the question was clear, everything fell in place! – Aravind Jul 05 '13 at 06:20
2
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).
jason
- 236,483
- 35
- 423
- 525