There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1. Puzzle (no spoilers till Sunday please!): What color is 355/113? Jim Propp
Argh: 355/113 isn't in [0,1]; replace it by 113/355. Jim On Friday, April 15, 2016, James Propp <jamespropp@gmail.com> wrote:
There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1.
Puzzle (no spoilers till Sunday please!): What color is 355/113?
Jim Propp
It appears that the coloring can be extended to all rationals. --Rich ------------ Quoting James Propp <jamespropp@gmail.com>:
Argh: 355/113 isn't in [0,1]; replace it by 113/355.
Jim
On Friday, April 15, 2016, James Propp <jamespropp@gmail.com> wrote:
There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1.
Puzzle (no spoilers till Sunday please!): What color is 355/113?
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
You're basically right. But isn't there some ambiguity about negative rationals? E.g., what color is -1, and why? Jim On Saturday, April 16, 2016, <rcs@xmission.com> wrote:
It appears that the coloring can be extended to all rationals. --Rich
------------ Quoting James Propp <jamespropp@gmail.com>:
Argh: 355/113 isn't in [0,1]; replace it by 113/355.
Jim
On Friday, April 15, 2016, James Propp <jamespropp@gmail.com> wrote:
There's a unique way to 3-color the rationals in [0,1] using the colors
red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1.
Puzzle (no spoilers till Sunday please!): What color is 355/113?
Jim Propp
_______________________________________________ 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
Keith Lynch was the first to solve this puzzle (or at least the first to email me a solution). Rich Schroeppel pointed out that the restriction to [0,1] is unnecessary. It's now Sunday where I am, so Keith and others may post freely. Jim Propp On Friday, April 15, 2016, James Propp <jamespropp@gmail.com> wrote:
There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1.
Puzzle (no spoilers till Sunday please!): What color is 355/113?
Jim Propp
You need some Stern-Brocot action for this one. On Sun, Apr 17, 2016 at 6:40 AM, James Propp <jamespropp@gmail.com> wrote:
Keith Lynch was the first to solve this puzzle (or at least the first to email me a solution).
Rich Schroeppel pointed out that the restriction to [0,1] is unnecessary.
It's now Sunday where I am, so Keith and others may post freely.
Jim Propp
On Friday, April 15, 2016, James Propp <jamespropp@gmail.com> wrote:
There's a unique way to 3-color the rationals in [0,1] using the colors red, blue, and green so that 0 is red, 1 is blue, and the fractions a/b, c/d, and (a+c)/(b+d) all have distinct colors whenever ad-bc=1.
Puzzle (no spoilers till Sunday please!): What color is 355/113?
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Allan Wechsler -
James Propp -
rcs＠xmission.com