Lib (libram) wrote in pencilpuzzlers,
Lib
libram
pencilpuzzlers

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Math problem

A friend started me on a crazed math problem that I'm racking my brains over.

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.
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