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# A Calendar Trick!

By inquisitive | Published | No Comments

I love clever Maths tricks…and this one is a very simple one to amaze your friends and family with. Challenge your friends to beat you to some mental arithmetic, and you will win every time!

So what do you need to do?

Take a calendar, pick a month and draw any 3×3 block around numbers in that month so that each square contains a number (i.e. it doesn’t go outside the dates).

I bet I can add up all the numbers in the circled box quicker than you can! Get your calculator out – or use your internal calculator – and get adding…but by the way the answer is 162…

The trick is simple. Simply look at the middle number in the square and multiply it by 9 – and you’ll get your answer. So in the above example, 18 x 9 = 162. If you just want the trick, then leave it there. And to multiply quickly by 9 – just multiply the number by 10 and take away the original number e.g. 17 x 9 = 17 x 10 – 17 = 170 – 17 = 153.

But why does it work? For each group of 3 numbers in a row, the sum is equal to 3 x the middle number as they are consecutive. Since the numbers in the top row are 7 less than the middle row, and those in the bottom row are 7 more than the middle row, this averages out to simply adding the middle number 9 times. For a more mathematical proof, let x be the middle number. Then the numbers either side are ‘x-1’ and ‘x+1’. And you can similarly take the top row to be ‘x-8’, ‘x-7’ and ‘x-6’, and likewise for the bottom row ‘x+8’, ‘x+7’ and ‘x+6’. If you add all these terms together, you get 9x!

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