A noteworthy feature of this year's contest was the presentation of a Helaman Ferguson sculpture which will serve as a trophy to travel to the winning school each year. The sculpture uses 16 pieces in two colors of polished granite to illustrate a dissection proof of the pizza theorem (see Mathematics Magazine. 67(1994)267).

Results: 1. Carleton #1 70 pts Daniel Martin and Neal Weiner 2. Carleton #2 68 pts John Costello, Curtis Mitchell, Liz Stanhope 3. Macalester #1 58 pts Michael Dekker, Sim Simeonov, Michael Wolfe 4. Carleton #3 44 pts 5. St. Olaf #1 34 pts 6. Carleton 4 32 pts 7. Macalester 2 25 pts 8. Macalester 2A 25 pts 9. St Olaf 2 16 pts 10. St Olaf 3 13 pts

Here is the complete text of the 1995 Konhauser Problemfest problems (which were selected by Stan Wagon from various places, mostly the old Konhauser files). The hardest ones from the point of view of the contest were #5, #6, #7, and #8. Wagon would have predicted that #8 was hardest, but two teams solved it. Only one team solved #6.

In the diagram, the large circle has radius one, the inscribed figures are a diameter (a), an equilateral triangle (b), and a square (c), the shaded circle is tangent to the top of the circle, and the other tangencies are as they appear. Determine the radii of the shaded and unshaded circles.

- If a + b = 0 and |a| = |b|, then a^2 = b^2.
- If a + b + c = 0 and |a| = |b| = |c|, then a^3 = b^3 = c^3.
- If a + b + c + d = 0 and |a| = |b| = |c| = |d|, then a^4 = b^4 = c^4 = d^4.

*Note:* A line L in 3-space is perpendicular to another
line M if M is contained in a plane perpendicular to L.

| | | | | | | ---------------------------------------- | 5 | 4 | 7 | 6 | 1 | 0 | ---------------------------------------- | 4 | 5 | 6 | 7 | 0 | 1 | ---------------------------------------- | 3 | 2 | 1 | 0 | 7 | 6 | ---------------------------------------- | 2 | 3 | 0 | 1 | 6 | 7 | ---------------------------------------- | 1 | 0 | 3 | 2 | 5 | 4 | ---------------------------------------- | 0 | 1 | 2 | 3 | 4 | 5 | ----------------------------------------

+--+-----+--+--+-----+ | | | | | | +--+--+--+ | +--+--+ | | | | | | | +-----+--+--+--+--+--+

- Problem 1 is a 1955 Leon Bankoff problem -- the result is quite surprising!
- Problem 3 is a Chinese Olympiad practice problem; from a recent issue of Crux Mathematicorum.
- Problem 8 was suggested by Phyllis Chinn of Humboldt State Univ.,
Arcata, Calif.
Here are some references:
- Robert C. Brigham, Richard M. Caron, Phyllis Z. Chinn, and Ralph Grimaldi, A tiling scheme for the Fibonacci numbers, Journal of Recreational Mathematics (to appear).
- Robert C. Brigham, Phyllis Z. Chinn, Linda Holt, and Steve Wilson, Finding the recurrence relation for tiling 2 x n rectangles, Congressus Numerantium (to appear)

- Problem 10 is an old U.S. Olympiad problem. The result is true if three is replaced by an odd integer.

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