IMC 2011 Q16
16. The diagram shows an L-shape divided into 1 × 1 squares.
Gwyn cuts the shape along some of the lines shown to make two pieces, neither of which is a square. She then uses the pieces to form a 2 × 6 rectangle.
What is the difference between the areas of the two pieces?
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2011, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 2
The L-shape needs to be divided as shown since neither of the pieces is to be a square. Notice that one of the pieces must be turned over. The difference between the areas of the two pieces is 7 − 5 = 2.
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).