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## Five Problem Play

In late August, 1990, The Oregon Council of Teachers of Mathematics hosted their Fourth Mathematics Chairpersons Retreat in Yamhill, Oregon. It was coordinated by the revered Wally Rogelstad.

At this retreat, John Dupasquier, a mathematics teacher at Rex Putnam High School, posed these Challenge Problems to the participants...

1. A horse is tethered to a rope at one corner of a square building 8 meters on a side. The rope is 11 meters long. Sketch a picture showing the maximum area the horse can graze. Find the area.
2. The perimeter os a right triangle is 60 cm. The length of the altitude to the hypotenuse is 12 cm. Find the lengths of the sides of the triangle.
3. The hands of a clock are together at noon. When will they be together again for the first time?
4. Find the highest power of 2 that divides 100!.
5. The host at a party turned to a guest and said, "I have three daughters and I will tell you how old they are. The product of their ages is 72. the sum of their ages is my house number. How old is each? The guest rushed to the door, looked at the house number and informed the host that he needed more information. The host then added, "The oldest likes strawberry pudding." The guest then announced the ages of the three girls. What are their ages?

Hint: Rather than a hint, I suggest that Problem #2 is perhaps the hardest, Problem #1 becomes easy once you draw the picture, Problem #3 is dated given today's clocks, while Problems #4 and #5 are the most fun (my view only, perhaps).

Solution Commentary: I will only provide the given answers, and note that not all of them are correct:

• 381/4
• 15, 20, 25
• 1:05:27.27
• 97
• 3, 3, 8