Problem of the Week 822

Numbering the Pentagram

Is it possible to place the ten numbers 1, 2, 3, ..., 10 (using each number exactly once) at the vertices of a pentagram, such that the sums of the numbers along the sides of the pentagram are the same? (These vertices can be considered the intersection points of 5 lines in general position in the plane).

                  0
                 x x
                x   x
      0xxxxxxxxx0xxxx0xxxxxxxx0
       x       x     x     x
          x   x       x  x
             0         0
            x  x    x  x
           x      0     x
          x    x     x   x
         x  x          x  x
        0                 0

Source: Leo Moser, Pi Mu Epsilon Journal.

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Which Way Did the Bicycle Go?

The book Which Way Did the Bicycle Go? by Joseph Konhauser (deceased), Dan Velleman (Amherst), and Stan Wagon (Macalester) is now finally available from the MAA. This book consists of 191 problems and solutions selected from the Problems of the Week at Macalester College from 1968 to 1995.

The book is especially rich in figures (183 B/W figures, 3 B/W photographs, 2 color photographs of coins for a coin problem, and one color diagram for an Erdõs problem).

Dolciani series, volume 18. 237 + xv pages.
ISBN 0-88385-325-6
$19.95 for MAA members, $24.95 for nonmembers
To order, call 800-331-1622 or visit http://www.maa.org.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998