Puzzles have existed since the times of the ancient Greeks and Romans. Mathematical puzzles by the Greek mathematician Euclid, Pythagorous, or the Vedic scholar Bodhayana eventually evolved into accepted mathematical facts.
Puzzles are found in all schools; only there they are called quizzes or tests. How to measure out one litre of liquid using only three containers, each of different a size (size varies from test to test and is immaterial. It is the math that counts; pardon the pun.).
Or the many variation of “How many” puzzles, such as: “If there were as many of us again and fifty percent as many more there would be 30 of us. How many are we?
Another example is: Every widget is a giget. One-half of all gigets are widgets. One-half of all zigets are gigets. There are 30 zigets and 20 gigets. All widgets are zigets. How many gigets are not widgets or zigets.
Here is a variation on number game puzzles: Think of a number, triple it, divide result by two, triple the answer and take one-half of the result. Now divided that by nine and the result will always be one-quarter of the original number.
Mathematical challenges of ancient and more recent times can be found in puzzles such as ticktacktoe, sliding square games, or find a number games.
Puzzles have been, and are today, created to pose a challenge and/or provide intellectual joy; that mental pat on the back one receives after solving a puzzle.
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