by mike

I was reading about Friedman numbers a few days ago. They are numbers where you can place mathematical symbols around the digits to create an expression whose value is equal to the original number.

For example, 127 is a Friedman number because you can write:

-1 + 2^7 = 127.

16384 is another: 16^3 x 8 / √4 = 16384.

That one was easy because I knew 16384 is a power of 2. Other numbers on the list of puzzles I found were either easy because I knew something about the number (343 for example I know is a power of 7), fairly easy because I can factor them and get clues, or rather difficult because the numbers are unfamiliar.

That got me thinking about two-digit Friendman numbers. I thought they'd be a lot easier to find. Turns out they're pretty hard to find!

I have found six so far. I wonder if hubski can find more. I won't post any of my 6 right away. Maybe you'll find it as fun as me?

As a clue, I offer that the *factorial* and the *double factorial* funtions are useful. The factorial function is well-known. 4! for example = 4 x 3 x 2 x 1 = 24.

The double factorial is not well known but comes in very handy in this puzzle. Double factorial is like a "skip factorial", it is the product of every other integer equal to the number you're operating on down to 1 or 2. So for an even number n, n!! is the product of all the even numbers less than or equal to n. And for n odd, n!! is the product of all the odd numbers less than or equal to n. Examples are maybe better than notation, so for example:

8!! = 8 x 6 x 4 x 2 = 384

and 7!! = 7 x 5 x 3 x 1 = 105

I'd love to see what you find. I have two solutions for 48, and one of them is pretty crazy!