IMC 2019 Q2
2. Each of the five shapes shown below is made from five unit cubes.
Which has the smallest surface area?
Intermediate Mathematical Challenge 2019, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E
Before any of the cubes are joined, the total surface area of the five cubes is equal to 5 × 6 = 30. Whenever two faces are joined, the total surface area decreases by two. Figures A to D all contain four joins, but figure E has five joins and therefore has the smallest surface area, namely 20.
Solution © UK Mathematics Trust, from the IMC 2019 solutions. Longer versions with investigations: Solutions and investigations (PDF).