Problem of the Week 1008

Wine Bottle Problem, Revisited

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Start with a row of n congruent circles lying on a horizontal line. Place n-1 circles above them so that each one rests on two circles in the first row. Assume that the initial spacing is such that no circle in the second row, or higher rows, falls through the gaps. Now place n-2 circles above these so that each touches two of the circles in the second row. Continue until there is only one circle at the top. Show that the horizontal location of the top circle is exactly halfway between the two outermost bottom circles.

Source: Adam Brown, Havergal College (Math. Mag. 76 Oct 2003, p. 301-302)

© Copyright 2004 Stan Wagon. Reproduced with permission.