IMC 2020 Q7
7. Kartik wants to shade three of the squares in this grid blue and Lucy wants to shade the remaining two squares red. There are ten possible finished grids.
In how many of the finished grids are Lucy’s red squares next to each other?
- A 3
- B 4
- C 5
- D 6
- E 8
Intermediate Mathematical Challenge 2020, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 4
We label the five squares, from left to right, \(P, Q, R, S, T\) respectively.
In order to paint two adjacent squares, Lucy could paint \(P\) and \(Q\), or \(Q\) and \(R\), or \(R\) and \(S\), or \(S\) and \(T\). So in four of the finished grids, Lucy’s red squares are adjacent to each other.
Solution © UK Mathematics Trust, from the IMC 2020 solutions. Longer versions with investigations: Solutions and investigations (PDF).