Another Calendar Trick

Here’s a (relatively) simple math trick to impress your friends and family with your mental prowess.

The only props you’ll need are one of those month-by-month calendars and a calculator.

First, ask your friend to make a 3 x 3 square anywhere within the month. The only caveat is that each box must have a date number in it.

Then, have him tell you the starting date, that is, the number in the top left square of the 3 x 3 grid.

Okay?

Finally, after a pause of only a second or two, you’re able to tell him the sum of all nine dates in the box. After clumsily punching in the dates on the calculator, a minute later your friend is able to confirm your answer.

Wow!

How is it done?

It’s really just a simple algebra problem.

Let’s call the top left date in the 3 x 3 grid x. The next two days in that row are x + 1 and x + 2. Drop down to the second row. The three dates there are x + 7, x + 8, and x + 9. And for the third row, the dates are x + 14, x + 15, and x + 16.

Add them all up and you get: x + x + 1 + x + 2 + x + 7 + x + 8 + x + 9 + x + 14 + x + 15 + x + 16

Which reduces to 9 x + 72

Which further reduces to 9 (x + 8)

So when your friend tells you that top left date, x, add 8 to it and multiply that sum by 9. If multiplication by 9 is too hard, multiply by 10 and subtract the original number.

Example:

Let’s say the 3 x 3 calendar grid is

...7...8...9
..14..15..16
..21..22..23

The grand sum of the grid is 9 (7 + 8) = 9 x 15 = 150 – 15 = 135

A calculator will confirm this.

Aaaaaaaaamazinggggggggggg!!!

(See here for an additional calendar trick)