One of three friends gives the other two a puzzle. Mario says “I’ve thought of two different one-digit numbers. When you multiply these two numbers, the last digit of that is the same as the last digit of Lizzie’s house number. What’s the sum of these two one-digit numbers?"
Ioannis says “I don’t know Lizzie’s house number"
Then Lizzie says “Well, obviously I know my own house number. And now I’ve worked out the sum of the two numbers."
Finally Ioannis says “Ahh, I didn’t know the sum before, but now I
know the sum."
What’s the sum?