Permalink Submitted by Anonymous on September 19, 2014

For Base 2 an admittedly somewhat trivial solution becomes apparent if you append a final zero as you can in the case of any base b so that you get a final number divisible by b as well. So you can divide 1 by 1 in Base 2, and then 10 by 2 (ie divide 10 by 10 base 2) just as you can divide 3816547290 by 10 Base 10.

By my reckoning three of the solutions you give for octals are in error: 127456 and 561472 aren't divisible by 6, and in the last, 723 isn't divisible by 3.

But hey, the other three are three more than what I found!

Have you got anywhere with solutions for other bases? One clue is that for an even base b the middle number must be b/2, so 6 for base 12 as 5 for 10, 4 for 8 etc.

## Generalizing to other bases

For Base 2 an admittedly somewhat trivial solution becomes apparent if you append a final zero as you can in the case of any base b so that you get a final number divisible by b as well. So you can divide 1 by 1 in Base 2, and then 10 by 2 (ie divide 10 by 10 base 2) just as you can divide 3816547290 by 10 Base 10.

By my reckoning three of the solutions you give for octals are in error: 127456 and 561472 aren't divisible by 6, and in the last, 723 isn't divisible by 3.

But hey, the other three are three more than what I found!

Have you got anywhere with solutions for other bases? One clue is that for an even base b the middle number must be b/2, so 6 for base 12 as 5 for 10, 4 for 8 etc.