IMC 2011 Q12
12. What is the sum of the first 2011 digits when 20 ÷ 11 is written as a decimal?
- A 6013
- B 7024
- C 8035
- D 9046
- E 10057
Intermediate Mathematical Challenge 2011, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 9046
20 ÷ 11 = \(1\tfrac{9}{11}\) = 1.818181… . So the first 2011 digits are 1006 ‘1’s and 1005 ‘8’s. Therefore the required total is 1006 × 1 + 1005 × 8 = 1006 + 8040 = 9046.
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).