2008 HMMT November Guts Round Problem 26

John M. is sitting at (0,0), looking across the aisle at his friends sitting at (i,j) for each 1 \le i \le 10 and 0 \le j \le 5. Unfortunately, John can only see a friend if the line connecting them doesn't pass through any other friend. How many friends can John see?

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2008 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.