IMC 2020 Q9
9. Adam’s house number is in exactly one of the following ranges. Which one?
- A 123 to 213
- B 132 to 231
- C 123 to 312
- D 231 to 312
- E 312 to 321
Intermediate Mathematical Challenge 2020, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 312 to 321
Note that the numbers 123 to 213 are in both option A and option C. Also, numbers 213 to 231 are in both option B and option C, and numbers 231 to 312 are in both C and D. However, numbers 313 to 321 are in option E only. So that must be where Adam’s house is.
Solution © UK Mathematics Trust, from the IMC 2020 solutions. Longer versions with investigations: Solutions and investigations (PDF).