Question 1
Vinh and Khang have just received their mathematics IQ-test scores, which are natural numbers no greater than 20. They want to find out each other’s scores.
Vinh: “I know that the product of our scores is even.”
Khang: “I know that the product of our scores is divisible by 20.”
Vinh: “Then I am sure that our scores are different and their sum is greater than 20.”
Khang: “I still cannot work out your score, but I am sure that the average of our scores is greater than my score.”
Vinh: “Now I know your score. I can also tell you that the difference between our scores is divisible by 3.”
Khang: “Now I know your score too. You did very well. Congratulations!”
What is Vinh’s score?
Clarification for this version: the scores are positive whole numbers from 1 to 20. Initially each knows only their own score; both reason correctly and speak truthfully, taking account of everything already said.
Vinh: “I know that the product of our scores is even.”
Khang: “I know that the product of our scores is divisible by 20.”
Vinh: “Then I am sure that our scores are different and their sum is greater than 20.”
Khang: “I still cannot work out your score, but I am sure that the average of our scores is greater than my score.”
Vinh: “Now I know your score. I can also tell you that the difference between our scores is divisible by 3.”
Khang: “Now I know your score too. You did very well. Congratulations!”
What is Vinh’s score?
Clarification for this version: the scores are positive whole numbers from 1 to 20. Initially each knows only their own score; both reason correctly and speak truthfully, taking account of everything already said.