# Calculus

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What day of the week is 263 days from Monday? That is Monday 12-10-2007.

Is it Wednesday?

• Calculus -

7 days later it is again the same day of the week, so it is convenient to define a new number system in which
7 = 0. It turns out that you can do arithmetic in this new number system in the same way as in the ordinary number system.

If 7 equals zero, you can subtract 7 and still have the same number. So:

10 = 3

If you square both sides:

100 = 9 = 2

multiply both sides by 2:

200 = 4

Now, if you remember your multiplication tables, 63 = 9*7 = 0. Therefore 263 = 200 = 4

This means that 263 later it will be 4 days later in the week, i.e. Friday.

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