Re-running a fun, simple old golden-oldie from Alfred Posamentier's "Mathematical Amazements and Surprises":
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"You are seated at a table in a dark room. On the table there are twelve pennies, five of which are heads up and seven of which are tails up. (You know where the coins are, so you can move or flip any coin, but because it is dark you will not know if the coin you are touching was originally heads up or tails up.) You are to separate the coins into two piles (possibly flipping some of them) so that when the lights are turned on there will be an equal number of heads in each pile."
"Your first reaction is 'you must be kidding!' How can anyone do this task without seeing which coins are heads or tails up? This is where a most clever (yet incredibly simple) use of algebra will be the key to the solution."
Posamentier Continues:
"Let's 'cut to the chase' (You might actually want to try it with 12 coins.) Separate the coins into two piles, of 5 and 7 coins each. Then flip over the coins in the smaller pile. Now both piles will have the same number of heads! That's all! You will think this is magic. How did this happen. Well, this is where algebra helps us understand what was actually done."
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Explanation: ...At the start, there are 5 heads showing among 12 coins. After separating into piles, let's say the 7-pile now has "h" heads. The 5-pile then has "5 - h" heads, and "5 - (5 - h)" tails (or, just "h" tails). Once you flip the entire smaller pile, all the tails ("h" of them) become heads, and all the heads become tails. Thus you are left with "h" heads in the "5-pile," the same as the number in the "7-pile." Whaaa-laaahhhh! Math is a beautiful thang!!
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