Suppose A, B, and C are sets of tools needed by three workers on a job. For convenience, let’s call the workers A, B, and C. Suppose that A uses 8 tools, B uses 10 tools and C uses 5 tools. Further that, A and B share 3 tools, A and C share 2 tools and B and C share 2 tools. Finally, A, B, and C share the use of 2 tools. How many distinct tools are necessary to do a job?