Here's a math puzzler from the active mind of Otis Reedy. See if you can figure it out. Write your answer in your travel log, then click forward to the next page of the adventure. (Answers can be found in the Curriculum Connections pages for teachers under 'Math Connections'.)

"OK, fellow fruit jugglers, time for a little bit of mathematical magic: You and five of your classmates are toucans. You are about to line up side by side on a branch to play your customary fruit-passing game. Here's how you play: First everyone chooses a position in the line, from position #1 to position #6. Then one toucan gets to choose a number from 1-10 to determine how many times you will pass each fruit before eating it. For example, if the chosen number is 3, the toucans pass the fruit three times and the last toucan to receive it gets to eat it. This number (the number of passes) remains the same for ten pieces of fruit. To start the game, Toucan #1 picks the first fruit and begins the passing. After that, the toucan that eats a fruit picks the next fruit and begins the passing. The fruit is passed one toucan at a time, in order, from one end of the line to the other then back again (1-2-3-4-5-6-5-4-3-2-1-2-3.....). For today's game, you have chosen position #3 and it's your turn to choose a number from 1-10 to determine how many times the fruit will be passed before it is eaten. Which numbers would ensure that you get the most fruit possible? Which numbers would shut you out completely? Which numbers would spread the fruit out most equitably? What percentage of the time would you get the fruit if a) you chose an even number besides 10, and b) if you chose an odd number besides 5? Can you determine any patterns going on here? Can you determine a pattern of passing - or a rule change - that would allow each toucan to get an equal share of fruit? Have fun passing. Hope you get something to eat!"

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