A Howling Good Halloween Puzzle

Scenario

A Howling Good Halloween Puzzle

Many of you may have already seen a version of October's Problem to Ponder, a number puzzle that determines your age on the basis of the number of times that you want to eat chocolate per week. The October Problem to Ponder includes an additional challenge: Why does the puzzle work?

• How many times a week do you want to eat chocolate? (Pick more than one but less than 10 times).
• Multiply that number by 2.
• Add 5.
• Multiply that result by 50.
• If your birthday has occurred this year, add 1760 to that result. If your birthday is still to come this year, add 1759.
  (UPDATED for 2013: If your birthday has occurred this year, add 1763 to that result. If your birthday is still to come this year, add 1762.)  
• Subtract the year (all four digits) in which you were born.
• The result will be a three-digit number. The first digit will be the number of times a week that you want to eat chocolate, and the last two digits will be your age.

Extension: Suppose you wanted chocolate 10 or more times a week, or no chocolate at all. Could you still make the puzzle work?

Note to teachers: You can base the puzzle on anything that your students might want to do a number of times a week-for example, play video games, talk with or text friends, or read a book.