IMC 2014 Q13
13. How many numbers can be written as a sum of two different positive integers each at most 100?
- A 100
- B 197
- C 198
- D 199
- E 200
Intermediate Mathematical Challenge 2014, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 197
The smallest such number is 1 + 2 = 3, whilst the largest is 99 + 100 = 199. Every number between 3 and 199 may be written as 1 + \(n\) with \(n = 2, 3, \ldots, 99\) or as 100 + \(n\) with \(n = 1, \ldots, 99\). So in total there are (199 − 3) + 1 = 197 such numbers.
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).