Friday, February 29, 2008

A Puzzle for Leap Day, 2008 -- Can you make 97?

Today is February 29, a special date that only appears on our calendars every four years. There are exceptions to this 4 year rule on century years (those ending in 00). These years are NOT leap years unless the century is evenly divisible by 400. For example, 2000 was a leap year, but 2100 will NOT be. The cycle of leap years on our calendar repeats in a 400 year cycle. Within that cycle there will be 97 leap years.

All this historical information was a way to introduce this week's math puzzle.

Q: Using each of the digits in 2008 and standard math operations, can you write an expression that equals 97?
  • Each of the digits 2, 0, 0, 8 must be used. (2 and 8 will appear once, 0 will appear twice.)
  • You may use standard math operations of +, -, x, /, √(square root), ^(raise to a power) and !(factorial) along with parentheses for grouping.
  • Decimal points and multi-digit numbers may be used (e.g. 20, 208, .02 or 2.8
  • If squaring is done, that uses up the digit 2.
  • 0! is agreed to have a value of 1.
  • Anything raised to the zero power (i.e. x^0) is 1, but 0^0 may not be used (undefined)
  • The integer/floor/ceiling/round functions may NOT be used.
  • Change of bases may NOT be used.
  • Logarithms may NOT be used.
  • Sine and Cosine may NOT be used.
Edit: The answer is now available in the comments... but don't look if you still want to figure it out on your own.


  1. I can figure it out several ways with an extra 2, but not using just the digits available:


  2. You've got the idea but just aren't there yet. It is possible with exactly 4 digits, using the rules given. (P.S. There's a slight typo in your second equation.)

  3. Is there any specific strategy, without just guess and check?

  4. My stategy was to work backwards... you figure that you are 1 away from 96, that's a good number since it has lots of factors. So 0! + something...

    I then realized that 96 was 80% of 120. Hmm... and 120 is 5!, can I use that?

    (0! / .2)! * .8 + 0!

  5. Great solution. I started with the same premise - 96 was a good starting point. The connection between the factorial and percent eluded me. Thanks for an entertaining puzzle!


For NPR puzzle posts, don't post the answer or any hints that could lead to the answer before the deadline (usually Thursday at 3pm ET). If you know the answer, submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving. You can openly discuss your hints and the answer after the deadline. Thank you.