An athletics squad trains on a long straight track with dots marked at 10m intervals. the coach sets out cones on some of the dots for the squad's sprint training drills. she wants the squad to be able to run any distance which is a multiple of 10m, up to some maximum distance which depends on the number of cones. explain why it is not possible to place four cones a, b, c, d, in a line so that each multiple of 10m up to 70m can be run between two of the cones.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?