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Three university students, A, B and C, applied for a job in the computer laboratory. All were straightA students in both math and computer science. Since there was more than a month before the school year started, I devised a test to choose the best candidate.
On Day 1 I met with the 3 students and carefully explained the procedure. I had chosen a certain Pythagorean right triangle with integer sides. The hypotenuse was between 300 and 2300, inclusive. I would secretly tell A the length of the shorter leg, B the length of the longer leg, and C the length of the hypotenuse. Then I would ask them, in turn, if they could tell me the lengths of all 3 sides, giving them a full day each time to consider their answers. They would all hear the other students' answers.
On Day 2 I assembled the 3 students and asked A what are the lengths of the 3 sides. A did not know.
On Day 3 I assembled them and asked B for the lengths of the 3 sides. B did not know.
On Day 4 I asked C for the lengths of the 3 sides. C did not know.
On Day 5 I asked A again for the lengths of the 3 sides. A did not know.
I continued asking them in turn for lengths of the 3 sides. Finally, on Day 17, after I had asked A for the sixth time, and A did not know, both B and C shouted out "I know!"
What is the length of the shortest side?
For this you will need four pennies. Arrange the pennies so that the centers of all four are equidistant from each other.
Example:
(1) (2) (3) (4)
This will not work because penny 1 and penny 4 are farther apart than penny 1 and penny 2.
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