IMC 2012 Q1
1. How many of the following four numbers are prime?
3 33 333 3333
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2012, Question 1. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1
As 33 = 3 × 11, 333 = 3 × 111 and 3333 = 3 × 1111, none of 33, 333, 3333 is prime. So 3 is the only one of the four numbers which is prime.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).