IMC 2018 Q7
7. How many two-digit squares have the property that the product of their digits is also a square?
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2018, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1
The two-digit squares are 16, 25, 36, 49, 64, 81. The products of their digits are 6, 10, 18, 36, 24, 8, respectively. So exactly one two-digit square has the required property, namely 49.
Solution © UK Mathematics Trust, from the IMC 2018 solutions. Longer versions with investigations: Solutions and investigations (PDF).