BEBRAS 2023 Grade 9-10 Round 2 Ext Question 10

Question 10

Alice, Bob, Chris, Dani and Emily each have a secret number. The five numbers are distinct positive three-digit integers, each using three different digits from 1 to 5.
- If the hundreds digit is 4, the tens digit is not 3.
- The units digits of Alice, Dani and Emily are respectively 5, 2 and 3.
- The hundreds digits of Chris and Emily are respectively 5 and 2.
- If the units digit is 2, the hundreds digit is 4.
- Bob’s tens digit is 2.

Which list, in the order Alice, Bob, Chris, Emily, Dani, could give their numbers?

531 – 123 – 415 – 342 – 254
123 – 451 – 234 – 512 – 345
135 – 321 – 514 – 243 – 452
543 – 215 – 432 – 154 – 321