Puzzles for the New Year

As we all head back to school, here are some interesting calendar puzzles:

• 2008 is a leap year. Why do leap years happen? If we didn’t add a leap day every so often, would January eventually come in the summer?
• Today is Thursday. What day of the week will it be exactly one year from today?
• January 1, 2008, came on a Tuesday. When will be the next year that begins on Tuesday?
• My birthday (in March) lands on a Monday this year. When is the next year my birthday will come on a Monday? How about YOUR birthday — when is the next time it will happen on the same day of the week as this year?
• Can you find a pattern in the way dates move from one day of the week to another, year after year?

Calendar Magic

You can also do some cool magic tricks based on the calendar:

• Cynthia Lanius: Algebra Fun with Calendars
• and Design Your Own Puzzle
• Cut the Knot: Calendar Magic

Birthday Arithmetic

Test your arithmetic skills with this series of calculations:

Write the number of the month in which you were born.
Multiply by 4.
Add 13.
Multiply by 25.
Subtract 200.
Add the day of the month you were born.
Multiply by 2.
Subtract 40.
Multiply by 50.
Add the last two digits of the year you were born.
Subtract 10,500.

If you made no mistakes, the answer should give your birthday in mmddyy format. Now test your algebra skills:

• Can you explain why this works?

Finally, the 2008 Mathematics Game starts tomorrow. Don’t miss it!

[Spoiler alert: Answers to the first set of calendar puzzles above can be found here, here, there, and there, too, while the birthday arithmetic puzzle is here at Ask Dr. Math.]