IMC 2009 Q11
11. The diagram below shows a pattern which repeats every 12 dots.
Which of the following does the piece between 2007 and 2011 look like?
Intermediate Mathematical Challenge 2009, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E
Note that 2004 is a multiple of 3 (since its digit sum is a multiple of 3) and also a multiple of 4 (since its last two digits form a multiple of 4). So 2004 is a multiple of 12 and hence the part of the pattern between 2007 and 2011 is the same as the part of the pattern between 3 and 7.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.