Chapter 4.5, Problem 18P

* Try out this next mathematical magic trick. Do the following on a piece of paper:

a. Write the number of days a week you would like to go out (from I to 7).

b. Multiply the number by 2.

c. Add 5.

d. Multiply by 50.

e. If you have already had your birthday this year, add 1762 if it is 2012. (Add 1763 if it is 2013, add 1764 if it is 2014, and so on.) If you have not yet had your birthday this year, add 1761 if it is 2012. (Add 1762 if it is 2013, add 1763 if it is 2014, and so on.)

f. Finally, subtract the 4-digit year you were born. You should now have a 3-digit number. If not, try again. If you have a 3-digit number, continue with the following:

The first digit of your answer is your original number (i.e., how many times you want to go out each week). The second two digits are your current age.

Is it magic, or is it math? Explain why the trick works.