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the basement => the archives => Logic Puzzles => Topic started by: redyoshi49q on February 23, 2009, 09:57:00 pm

This would be another puzzle of mine that I have developed recently. It is inspired by a similar problem that I read in a puzzle book, but it has a nice little twist in it, as you will soon find out.
Please do *not* post ideas/solutions/etc. here for the courtesy of other puzzle solvers. Instead, feel free to post in the spoiler thread.
Commence take two!
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Billy and Bob, the elite puzzlists, are conversing at a table. After the formalities pass, Billy poses a puzzle to Bob.
"I have another puzzle for you today. It is a twist off a classic problem, which involved putting 31 apples in 5 bags..."
"Yeah, I know that problem. The first bag had one apple, the second had two, the third..."
"Yes, I figured you were familiar. This time, though, let's say that I have a specific but as of yet undetermined number of bags in my possession, with each bag having a number of apples. In order to give you an arbitrary number of apples, I can give you a specific combination of my bags."
"Obviously."
"With the set of bagged apples that I have, however, I am able to give you apples in this manner for each number of apples from 2 to 1,023 as well as the number 1,025. Without giving you apples outside of these bags or changing the number of apples in the bags, though, I cannot give you exactly 1 apple. It is also impossible for me to give you exactly 1,024 apples or any number of apples greater than 2,000. Having said that, my question to you is this: how many bags do I have, and how many apples do I have in each of these bags?"
After several minutes of intense thought, Bob gives Billy an answer, which is then deemed by Billy to be correct.
What is the answer to Billy's puzzle?