Andy draws the question card, “How many 7s do you see?” He answers, “one,” because he cannot see the 7 on his own head; he sees only the 7 on Belle's head.
Next Belle draws the question card, “ Of the four even numbers, how many different even numbers do you see?” She answers, “Three,” because she sees the 4, 6, and 8 on Andy and Dan's head.
From this, Dan can conclude he has two even cards, since he can only see a 6 and Belle sees two more.
What is your question?
Andy draws the question card, “How many 7s do you see?” He answers, “one,” because he cannot see the 7 on his own head; he sees only the 7 on Belle's head.
Next Belle draws the question card, “ Of the four even numbers, how many different even numbers do you see?” She answers, “Three,” because she sees the 4, 6, and 8 on Andy and Dan's head.
From this, Dan can conclude he has two even cards, since he can only see a 6 and Belle sees two more.
What cards do you have?
In answering this question, you must write a neat and professional report. You need to briefly summarize the salient facts of the problem, explain your strategy for solving the problem, explain why your strategy will work, execute your strategy, show your mathematical working, draw conclusions from your working, and finally present your answer with a brief summery of why it is your conclusion.
2. Remember, your strategy is to use more than logic. What kind of logic will you use?
To understand how Dan can conclude that he has two even cards, let's break down the information provided.
First, Andy draws a question card asking how many 7s he sees. He answers "one" because he can only see the 7 on Belle's head and not the one on his own.
Next, Belle draws a question card asking how many different even numbers she sees out of the four even numbers. She answers "three" because she can see the 4, 6, and 8 on Andy and Dan's head.
From Belle's answer, Dan can conclude that he has two even cards. This is because, according to Belle, she sees three even numbers (4, 6, and 8), which means that the remaining even number must be on Dan's head. Since Dan cannot see the even number on his own head, he can deduce that he has two even cards.
In this scenario, the key reasoning is based on the fact that Belle can see three even numbers, leaving only one even number (which belongs to Dan) unseen by either Belle or Andy. Hence, Dan can conclude that he has two even cards.