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HEXA Challenge Section Editor: Eric P. Choate

With every issue of Virginia Mathematics Teacher that is released, we include six HEXA Challenge questions. The answers to this issue will be featured in the 48(1) issue of the journal. See the section “ Solutions to 47(1) HEXA Challenge Problems ” towards the back of the journal for solutions to the problems featured in our previous issue.

Problems created by: Eric P. Choate, Charlene J. Galvez, Adam Downs

Challenge 1: Let C 1 be a circle of radius R . Let S be a square inscribed inside C 1 , and let C 2 be a circle inscribed inside S . A point is selected randomly from inside C 1 . Rank the following three outcomes from most likely to least likely.

1. The point is inside C 2 2. The point is outside C 2 but inside S. 3. The point is outside S.

Challenge 2: My watch is gold and belonged to my great - grandfather, and so I like to wear it even though it is not the most accurate timekeeper. This watch gains one second every five hours. I can live with this watch being accurate, with two minutes, and so every time the watch gets two minutes ahead of the actual time, I reset it to be two minutes behind the actual time. That is, at noon on January 1, my watch read 12:02, and so I reset it to 11:58. What day and time will I have to reset it again?

Challenge 3:

Solve the following system of equations for x and y.

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Virginia Mathematics Teacher vol. 47, no. 2

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