IMC 2009 Q21
21. There are lots of ways of choosing three dots from this 4 by 4 array. How many triples of points are there where all three lie on a straight line (not necessarily equally spaced)?
- A 8
- B 16
- C 20
- D 40
- E 44
Intermediate Mathematical Challenge 2009, Question 21. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 44
Consider the top row of four dots. One can obtain a triple of dots by eliminating any one of the four – so there are four such triples. The same is true for each of the four rows, each of the four columns and the two main diagonals, giving 40 triples. In addition there are four diagonal lines consisting of exactly three dots, so there are 44 triples in total.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.