A particle is set to move up or down 1 unit of length during 2,3, and 5 units of time. The particle starts moving from the origin making steps of unit length in 2, 3, or 5 units of time. Student 1 is asked to list all possible return times to the origin if the particle makes one move up or down every 2 units of time. Student 2 is asked to list all possible return times to the origin if the particle makes one move up or down every 3 units. Student 3 is asked to list all possible return times to the origin if the particle makes one move up or down in 5 units. Each of the students fills in his line in the table below. If each student is asked not to write down return times above 100, what is the total number of entries that the students make?
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student 1 possible return times
student 2 possible return times
student 3 possible return times
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a) none
b) 25
c) 50
d) 51
e) an infinite number of integers