[math-fun] Guess my numbers
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references. Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers? I got this wrong when I first heard it. Hint: The answer isn't n. Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away! Thanks, Jim
Do we need to figure out each x_i? Or only up to permutation? Or only the set (not multiset) of values? --Michael On Wed, Jan 6, 2016 at 11:06 AM, James Propp <jamespropp@gmail.com> wrote:
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references.
Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers?
I got this wrong when I first heard it. Hint: The answer isn't n.
Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away!
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
Figure out each x_i. Jim On Wed, Jan 6, 2016 at 11:18 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
Do we need to figure out each x_i? Or only up to permutation? Or only the set (not multiset) of values?
--Michael
On Wed, Jan 6, 2016 at 11:06 AM, James Propp <jamespropp@gmail.com> wrote:
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references.
Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers?
I got this wrong when I first heard it. Hint: The answer isn't n.
Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away!
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Can each question be based on the answers to the previous questions? On 06-Jan-16 11:06, James Propp wrote:
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references.
Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers?
I got this wrong when I first heard it. Hint: The answer isn't n.
Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away!
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Yes it can! (Assuming otherwise was my mistake, back in my teen years when I encountered the problem.) Jim On Wed, Jan 6, 2016 at 11:31 AM, Mike Speciner <ms@alum.mit.edu> wrote:
Can each question be based on the answers to the previous questions?
On 06-Jan-16 11:06, James Propp wrote:
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references.
Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers?
I got this wrong when I first heard it. Hint: The answer isn't n.
Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away!
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Ah, got it. OK, cute, and no I haven't seen it before. --Michael On Wed, Jan 6, 2016 at 12:21 PM, James Propp <jamespropp@gmail.com> wrote:
Yes it can! (Assuming otherwise was my mistake, back in my teen years when I encountered the problem.)
Jim
On Wed, Jan 6, 2016 at 11:31 AM, Mike Speciner <ms@alum.mit.edu> wrote:
Can each question be based on the answers to the previous questions?
On 06-Jan-16 11:06, James Propp wrote:
This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references.
Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers?
I got this wrong when I first heard it. Hint: The answer isn't n.
Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away!
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
participants (4)
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James Propp -
Michael Kleber -
Mike Speciner -
William R. Somsky