IMC 2011 Q3
3. The consecutive digits 1, 2, 3, 4 in that order can be arranged to make the correct division, 12 ÷ 3 = 4. One other sequence of four consecutive digits \(p\), \(q\), \(r\), \(s\) makes a correct division, ‘\(pq\)’ ÷ \(r\) = \(s\). What is the value of \(s\) in this case?
- A 4
- B 5
- C 6
- D 7
- E 8
Intermediate Mathematical Challenge 2011, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 8
12 ÷ 3 = 4, but this is the example given in the question. 23 ÷ 4 ≠ 5; 34 ÷ 5 ≠ 6; 45 ÷ 6 ≠ 7. However, 56 ÷ 7 = 8, so \(s\) = 8.
{Note also that 67 ÷ 8 ≠ 9.}
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).