IMC 2017 Q3
3. How many squares have 7 as their units digit?
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2017, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 0
Consider the units digits of the squares of the integers 0, 1, 2, 3, ..., 9. These are 0, 1, 4, 9, 6, 5, 6, 9, 4, 1. Note that none of these is 7, so no square ends in a 7.
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).