Comments on: One, Two, Three, Four, Six(?) http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/ 12 tables, 24 chairs, and plenty of chalk Thu, 30 May 2013 02:26:42 +0000 hourly 1 http://wordpress.com/ By: jd2718 http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/#comment-1507 Mon, 20 Oct 2008 02:54:52 +0000 http://threesixty360.wordpress.com/?p=1203#comment-1507 Arches up in the middle, divided by something… Let me verify that it holds for the next few numbers, and then I’ll post…

Jonathan

]]> By: Ξ http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/#comment-1506 Mon, 20 Oct 2008 00:49:16 +0000 http://threesixty360.wordpress.com/?p=1203#comment-1506 What pattern are you getting?

]]> By: jd2718 http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/#comment-1505 Mon, 20 Oct 2008 00:20:40 +0000 http://threesixty360.wordpress.com/?p=1203#comment-1505 I’m getting a weird pattern in Pascal’s triangle. I guess I should go play with it more.

]]> By: Ξ http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/#comment-1493 Thu, 16 Oct 2008 10:44:13 +0000 http://threesixty360.wordpress.com/?p=1203#comment-1493 It has to do with what you define to be “the same” or “different”. In this problem the clasp is hidden, so you can take that middle necklace and rotate it 180° and then the purple and gold will be on opposite sides.

Likewise, in the necklace with two purple and one gold bead, you can rotate it around so that the gold bead is in one of the other spots.

(If you didn’t allow the necklaces to rotate, then there would be one way with 0 beads, two ways with 1 bead, four ways with 2 beads [PP, PG, GP, GG], eight ways with 3 beads [PPP, PPG, PGP, GPP, PGG, GPG, GGP, GGG], and sixteen ways with 4 beads).

]]> By: Lambchop http://threesixty360.wordpress.com/2008/10/15/one-two-three-four-six/#comment-1492 Thu, 16 Oct 2008 05:38:37 +0000 http://threesixty360.wordpress.com/?p=1203#comment-1492 I guess with 2 beads, for example, position on the ring (left or right) is not significant. If it were, you’d have to add at least one more configuration: purple on the right and gold on the left. How come it doesn’t matter?

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