SOLUTION: students arrieve for the first day of school and meet in the gym, they find 300 pennies arranged on a long table in a long row. Each penny is facing heads up and is labled penny #1

Question 473821: students arrieve for the first day of school and meet in the gym, they find 300 pennies arranged on a long table in a long row. Each penny is facing heads up and is labled penny #1, penny #2, penny#3 ect. As each student passes along the table, they turn over only the pennies that match their number in line. For example student #1 turns over all the pennies; student #2 turns over all penny numbers divisible by 2; student #3 turns over all penny numbers divisible by 3; ect. You are to IDENTIFY the SET of all penny numbers that are HEADS UP after all three hundered students have passed by the table??
can you please help with this one??
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For some penny n, 1 <= n <= 300, it will be flipped over k times, where k is the number of factors of n. Also, if k is even, the penny will remain heads up, if k is odd, the penny will be facing tails up. Only perfect squares have an odd number of factors, so all numbers that are not perfect squares have an even k, and will remain heads up.
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