# Math in Christmas: The Present and the Future

For December 25, 2016, the day of the week is $$d_{\text{present}}$$.

For December 25, 6102, the day of the week is $$d_{\text{future}}$$.

If each type of days is denoted by the following:

• $$2 = \text{Sunday}$$
• $$3 = \text{Monday}$$
• $$5 = \text{Tuesday}$$
• $$7 = \text{Wednesday}$$
• $$11 = \text{Thursday}$$
• $$13 = \text{Friday}$$
• $$17 = \text{Saturday}$$

What is $$\left|d_{\text{present}} - d_{\text{future}}\right|$$? Try not to use the calendar to work this problem out!

Note: The calendar is Gregorian.

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