# ALGEBRA

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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.

• ALGEBRA -

• ALGEBRA -

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?