The following are the first four strings of numbers:
10 -> 1
25 -> 10 -> 1
39 -> 27 -> 14 -> 4
77 -> 49 -> 36 -> 18 -> 8
Notice that in each row there's one more arrow than the last. The arrows stand for multiplying all the digits in the first number, for example:
77 (7x7=49) 49 (4x9=36) 36 (3x6=18) 18 (1x8=8) 8
The challenge is to find the smallest number that has FIVE arrows/steps to get to a single digit number.
I found a five-step number (without the use of a program), but I don't know if it's the smallest:
6779 -> 2646 -> 288 -> 128 -> 16 -> 6
I'm a bit tired mentally to find another, smaller number with five steps, but maybe some of you can share my retarded pain and try this nerdy exercise out for yourselves.
Writing a program for it is cheating. Use your brain for this one.