A Free Thinking Skills Puzzle for Gifted Kids

Okay, here is a cool thinking skills puzzle you can do with your gifted students. The thinking skills puzzle below comes from this book (you can't order the book yet; we're still editing it and laying it out -- I'll let you know when it's available for preorders). Anyway, try this with your kids this week -- it's a good "hook" (what the author calls his thinking challenges) to get a classroom thinking.
Hook: You have two identical beakers, each holding an identical amount of fluid. One beaker holds red fluid, the other blue fluid. You take 1 tablespoon of the red fluid, drop it into the blue fluid and mix it up thoroughly. You then take 1 tablespoon of this mixture, drop it back into the red fluid and mix it up thoroughly. Question: Do you now have more red fluid in the predominantly blue beaker, more blue fluid in the predominantly red beaker, or are there equal amounts in each?
Solution: Equal amounts. Although the quantity in each beaker is irrelevant, let us assume, that, to begin with, each beaker has 9 tablespoons of fluid. In step one we transfer 1 tablespoon of red fluid to the blue beaker. We now have 10 tablespoons of fluid in that beaker, one-tenth of which is red and nine-tenths of which is blue. We now transfer 1 tablespoon of that mixture back into the red beaker. That tablespoon is one-tenth red and nine-tenths blue, so we have actually transferred one-tenth of a tablespoon of red fluid back intothe red container, making the net amount of red fluid left in the blue container nine-tenths of a tablespoon. When we transferred the mixture into the red container, that tablespoon was one-tenth red and nine-tenths blue, so the net amount of blue we transferred into the red container was also ninetenths of a tablespoon. Not as easy as it seemed at first, eh?
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