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In a local elementary school, jelly beans have become the most important means of barter. There are three flavors of jelly beans— apple, blueberry, and cherry. The students are very protective of their beans, and will not make any trade unless it seems like they are getting the better of the deal. However, they don't like to take advantage of anybody, so they won't make a deal if they are getting even one more bean than they think they ought to.

While students in different grades have different preferences, students in the the same grade all have the same preferences. There are six grades, and the type of trade each will make is shown below. No other trade is possible, and the trades are not reversible.
• 1st graders will give you 2 blueberry jelly beans and 3 cherry jelly beans for 1 apple jelly bean.
• 2nd graders will give you 3 cherry jelly beans and 1 apple jelly bean for 1 blueberry jelly bean.
• 3rd graders will give you 4 apple jelly beans and 1 blueberry jelly bean for 1 cherry jelly bean.
• 4th graders will give you 1 apple jelly bean for 5 blueberry jelly beans and 9 cherry jelly beans.
• 5th graders will give you 1 blueberry jelly bean for 2 cherry jelly beans and 7 apple jelly beans.
• 6th graders will give you 1 cherry jelly bean for 3 apple jelly beans and 4 blueberry jelly beans.
You walk into the auditorium holding a single apple jelly bean. By completing a sequence of trades with several students, is it possible for you to acquire only cherry jelly beans? If so, what is the minimum number of trades you'll have to make? Can you handle the other conversion tasks asked of you?

If you try to get rid of jelly beans by eating or discarding them, you will get detention. You may assume that the students have very deep pockets, with enough beans for any trade you want to make.

If you need help with the applet, press the ? button. Or follow the link below for how to solve these puzzles. The different conversion tasks can be selected from the Puzzle Choice pop-up menu.
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