IMC 2018 Q1
1. Which of these is the sum of the cubes of two consecutive integers?
- A 4
- B 9
- C 16
- D 25
- E 36
Intermediate Mathematical Challenge 2018, Question 1. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 9
The positive sums of cubes less than the largest option, 36, are \(0^3 + 1^3 = 1\); \(1^3 + 2^3 = 1 + 8 = 9\) and \(2^3 + 3^3 = 8 + 27 = 35\). Hence the correct answer is 9.
Solution © UK Mathematics Trust, from the IMC 2018 solutions. Longer versions with investigations: Solutions and investigations (PDF).