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How many points can you place? (Posted on 2004-01-16) Difficulty: 5 of 5
A solitaire game is played with the following rules:

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.

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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2007-06-25 12:28:22
SolutionTHAT'S EASY(the points game)kirk smith2004-04-14 22:05:50
re(2): Solution (Infinite Points)Paul2004-01-21 11:38:35
This problem is also known as ...Brian Smith2004-01-21 10:54:39
re: Nonuniform Epsilon?TomM2004-01-21 10:53:31
QuestionNonuniform Epsilon?Richard2004-01-20 18:22:37
Possible correction to infinite point solutionTomM2004-01-20 06:17:55
re: Solution (Infinite Points)exoticorn2004-01-20 02:52:12
Solution (Infinite Points)Paul2004-01-20 01:06:18
re: My algorithm (correction)TomM2004-01-18 13:20:58
My algorithmTomM2004-01-18 12:47:21
re(2): Solutionexoticorn2004-01-18 06:36:27
Questionre: SolutionSilverKnight2004-01-17 22:29:00
SolutionSolutionexoticorn2004-01-17 17:08:52
Six point counter-exampleTomM2004-01-17 13:03:34
Some Thoughtsre(4): Solution (I think !)Penny2004-01-17 10:36:59
re(3): Solution (I think !)TomM2004-01-17 09:41:27
Some Thoughtsre(2): Solution (I think !)Penny2004-01-17 03:32:15
re: Solution (I think !)TomM2004-01-17 02:58:28
re(2): Solution (I think !)Penny2004-01-17 02:33:21
Some Thoughtsre: Solution (I think !)SilverKnight2004-01-17 02:21:45
Some ThoughtsSolution (I think !)Penny2004-01-16 19:17:33
re: A possibilitySilverKnight2004-01-16 17:09:36
A possibilitydraistal2004-01-16 16:46:46
Some ThoughtsFood for thoughtSilverKnight2004-01-16 14:20:05
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