Brain Teasers
The Magic Shop
Fun: (2.26)
Difficulty: (2.18)
Puzzle ID: #4066
Submitted By: GoldieLuvNeopets Corrected By: fishmed
Submitted By: GoldieLuvNeopets Corrected By: fishmed
One day a mysterious figure burst into Laura's Magic Shop and posed her with a puzzle.
Slapping down a huge amount of money on the counter, he said "Divide $1083 (in whole dollar increments) into a number of bags, so that I can ask for any amount between $1 and $1083, and you can give me the proper amount by giving me a certain number of these bags without opening them.
If you are correct, you keep the money. If you aren't, you owe me one of your special potions..."
Laura took the challenge, being a very smart girl. What is the minimum number of bags Laura will require?
Slapping down a huge amount of money on the counter, he said "Divide $1083 (in whole dollar increments) into a number of bags, so that I can ask for any amount between $1 and $1083, and you can give me the proper amount by giving me a certain number of these bags without opening them.
If you are correct, you keep the money. If you aren't, you owe me one of your special potions..."
Laura took the challenge, being a very smart girl. What is the minimum number of bags Laura will require?
Answer
11 bags, filled as follows.1, 2, 4, 8, 16, 32, 60, 64, 126, 256, 512
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Comments
That is only half the answer, the real puzzle is in working out how much was in each of the eleven bags. With out that info your answer is quite redundant.
May 16, 2002
It's sorta a binary problem. If you put in the bags, 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512 in the first 10 bags you can make any amount from $1 to $1023. Throw the other $60 in the 11th bag to make up the difference (since you can already make any number from 964 to 1023 in the first 10 bags adding 60 will fill out the remaining numbers from 1024 to 1083) and you're all set.
Thanks for that KALIEL, I already knew the answer as I had seen the puzzle several times before. My comment was to the submitter about only half answering the puzzle.
YET AGAIN, ANOTHER STEAL OFF OF NEOPETS.COM
Mad, don't pick on Goldie. it might not be her fault that the answer isn't complete, they might not have had all of it on neopets! :-)
I removed the answer in the comments as I corrected the teaser to reflect what was missing.
I only knew the answer because I knew binary. That's practically the whole basis of why binary can work.
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