##### Nov 09, 2009

**RAY:**This was from my number 4 series. There's an old puzzler from long, long ago, and it went like this: Take the number 4, and using it five times, write a mathematical expression that will give you the number 55. Now it's pretty challenging because 4's an even number and 5's an odd number. How do you get 55 out of five 4's? And the answer is 44 + 44/4.

Jim Adams suggested something a little more challenging. He says, 'Take the number 4, use it 3 times, and write a mathematical expression that will give you the number 55.'

Now you can use any of the mathematical terms that are usually used in writing mathematical expressions: plus sign, minus sign, multiplication, division, square root -- you can't square anything because you'd be introducing the number 2 then. You can only use 4s. Your expression could have any of the symbols. You could have 4 to the 4th, you could have 4 factorial, you could have 4.4. You can use anything that you'd see in a mathematical expression as fair game.

What's the equation?

Answer:

**RAY:**Here's the answer: use four factorial. Now factorial means four times three times two times one. And that happens to equal 24. Now subtract from that the square root of 4 which happens to be two. So now you wind up with 22. And you have one 4 left, how are you going to do this? You divide 22 by 0.4.

**TOM:**Oh.

**RAY:**So it's 4 factorial, minus the square root of 4 all over 0.5, and that gives you 55.

**TOM:**Wow.

**RAY:**And I'm sure we'll get 5 - 6,000 emails for all the other ways to do it, but do we have a winner?

**TOM:**Hah. Our winner this week is Linda Snyder from Alamosa, Colorado. And for having her answer selected at random from among all the correct answers that we got, Linda is going to get a $26 gift certificate to the Shameless Commerce Division at cartalk.com, with which she can get a copy of our latest CD, Stairway to Heapdom.

**RAY:**Congratulations Linda!