Friday, February 29, 2008

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

2008 = 97Today 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?
Rules:
  • 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.

6 comments:

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

    ((8-0!)^2)*2-0!=97
    or
    (0!+2)!*8*2-0!=97

    ReplyDelete
  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.)

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

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  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?

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

    ReplyDelete
  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!

    ReplyDelete