SOLUTION: Notice that any four numbers once drawn in a square on a calender have the property bc-ad=7 for example: 13 14 20 21 20x14-13x21 = 280-273 =7

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Question 955734: Notice that any four numbers once drawn in a square on a calender have the property bc-ad=7
for example: 13 14
20 21
20x14-13x21
= 280-273
=7
This works for any four numbers drawn in a square if they are set out like:
a b
c d
so how do you mathematically prove that bc-ad=7 for any of the four numbers?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the upper left corner of the square.
Let's call that number, x.
The one to the right would be, x%2B1.
The one below x would be x%2B7.
And the one to the right of it would be x%2B8.
%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29=%28matrix%282%2C2%2Cx%2Cx%2B1%2Cx%2B7%2Cx%2B8%29%29
So now you can solve the problem algebraically.
bc-ad=%28x%2B1%29%28x%2B7%29-x%28x%2B8%29
bc-ad=%28x%5E2%2B7x%2Bx%2B7%29-%28x%5E2%2B8x%29
bc-ad=x%5E2%2B8x%2B7-x%5E2-8x%29
bc-ad=highlight%287%29%29