The Tic-Tac-Toe Magic Square trick

In Mathematics Magic and Mystery by Martin Gardner, the author presents an interesting card trick to create a magic square (where all rows and columns add to the same number), using an interesting interactive game with a participant. After playing a game of tic-tac-toe, your friends will be surprised to see they set up the cards in a 3×3 grid summing the number on the cards to 15!

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Sum/product of consecutive numbers and other math shortcuts

If you have studied some of the old SAT questions at some point you may have gone through questions like –

4 consecutive numbers sum to 166. What is the product of the numbers? or…

3 consecutive even numbers sum to X. What is their product?

The way the tutors and the online tutorials show seems to always be to algebraically solve this – for example 4 consecutive numbers would solve x+x+1+x+2+x+3 = 166, collect terms and solve…

However there is another way that works for this and works for other similar problems.

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