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 How many points can you place? (Posted on 2004-01-16)
A solitaire game is played with the following rules:
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On a line segment (of arbitrary length, set it as long as you wish, but for convenience/reference sake, let's say it extends from 0 to 1 on the number line), you place a point anywhere you like on it.

Now place a second point, such that either of the two points is within a different half of the line segment. (The halves are taken to be "open intervals", which means that the end points are not considered "inside" the interval.)

Place a third point so that each of the three is in a different third of the line.

At this point, you may notice that the first two points can't be just anywhere. They cannot, for example, be close together in the middle of the line or close together at one end. They must be carefully placed so that when the third point is added, each will be in a different third of the line.

You proceed in this way, placing every nth point so that the first n points always occupy different 1/nth parts of the line.
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If you choose locations carefully, how many points can you put on the line?

 See The Solution Submitted by SilverKnight Rating: 4.2000 (10 votes)

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 Subject Author Date Answer K Sengupta 2007-06-25 12:28:22 THAT'S EASY(the points game) kirk smith 2004-04-14 22:05:50 re(2): Solution (Infinite Points) Paul 2004-01-21 11:38:35 This problem is also known as ... Brian Smith 2004-01-21 10:54:39 re: Nonuniform Epsilon? TomM 2004-01-21 10:53:31 Nonuniform Epsilon? Richard 2004-01-20 18:22:37 Possible correction to infinite point solution TomM 2004-01-20 06:17:55 re: Solution (Infinite Points) exoticorn 2004-01-20 02:52:12 Solution (Infinite Points) Paul 2004-01-20 01:06:18 re: My algorithm (correction) TomM 2004-01-18 13:20:58 My algorithm TomM 2004-01-18 12:47:21 re(2): Solution exoticorn 2004-01-18 06:36:27 re: Solution SilverKnight 2004-01-17 22:29:00 Solution exoticorn 2004-01-17 17:08:52 Six point counter-example TomM 2004-01-17 13:03:34 re(4): Solution (I think !) Penny 2004-01-17 10:36:59 re(3): Solution (I think !) TomM 2004-01-17 09:41:27 re(2): Solution (I think !) Penny 2004-01-17 03:32:15 re: Solution (I think !) TomM 2004-01-17 02:58:28 re(2): Solution (I think !) Penny 2004-01-17 02:33:21 re: Solution (I think !) SilverKnight 2004-01-17 02:21:45 Solution (I think !) Penny 2004-01-16 19:17:33 re: A possibility SilverKnight 2004-01-16 17:09:36 A possibility draistal 2004-01-16 16:46:46 Food for thought SilverKnight 2004-01-16 14:20:05

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