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 Marble-Go-Round (Posted on 2004-12-28)
Consider N holes arranged in a circle on a wooden board. A marble is placed in one of them. You toss a fair coin to determine if you should move the marble one hole clockwise or one hole counterclockwise. You keep doing this until the marble has been in each hole at least once.

What is the probability that each of the N holes turns out to be the last hole visited by the marble? Number the holes 1 through N, clockwise starting with the hole in which the marble starts. Obviously the probability for hole 1 is zero, since it already has the marble and there are other holes to visit still.

 No Solution Yet Submitted by neshal Rating: 3.2000 (5 votes)

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 re(2): solution (spoiler) | Comment 3 of 4 |
(In reply to re: solution (spoiler) by Hugo)

The results I got for 100,000 trials (I didn't count the tosses) are:

` 1             0 2             11144 3             11049 4             11198 5             11073 6             11020 7             11089 8             11141 9             11115 10            11171`

with the program:

FOR trial = 1 TO 100000
tr = tr + 1
REDIM visited(10)
visited(1) = 1
visitCt = 1
posn = 1
DO
dir = (INT(2 * RND(1)) - .5) * 2
posn = posn + dir
IF posn < 1 THEN posn = posn + 10
IF posn > 10 THEN posn = posn - 10
IF visited(posn) = 0 THEN
visited(posn) = 1
visitCt = visitCt + 1
END IF
LOOP UNTIL visitCt = 10
NEXT
FOR i = 1 TO 10
NEXT
PRINT

 Posted by Charlie on 2005-01-02 17:33:23

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