Question 207361
Some friends decided to make a week-long bike trip, with some of them leaving or joining the trip long the way.  Two-thirds of the group wanted to try and go the entire distance.  After the first day 1/3 of the bikers left. On the second day, they got 8 new bikers.  At the end of the second day, they lost 3/7 of the group. On the third day they gained 2 new bikers and at the end of the day 2/5 of the group left.  Five new bikers joined up on the fourth day and they lost 3 at the end of the day.  On the fifth day, they picked up 4, and then lost 1/4 of the total group.  On the sixth day they got 4 new ones and at the end of the day 6 departed.  On the seventh day, 7 bikers finished the trip.  Did the group that wanted to go the whole way make it?
:
Obviously not.  7 is not {{{2/3}}} of an integer