A Puzzle for you.

Hi.

Here's a puzzle for you. The numbers

1174419192328135317274255658153198080427934304578038090 1680418304689456 6787292800844355644360850267694083886151344689499579001 3601143904693819 9997085476755

and

1548698505844910505316440847476718560478608108467963380 3451879461400354 9805894953276361189463850906775276855316001248612140851 4768101808558827 11408487828

have something special about them, namely about their quotient. Can you figure out what it is?

mike3 schrieb:

The numbers are relatively prime, but why is 75.83... special?

Cheers

It doesn't appear to be, but 75.8326548321564532108210546328764321812865318732658742 1674213675984 6321875999999000000000000000000000011111111110000000001 0000001000000 0000100000010000000000100000010000000000100000010000000 0000000000000 0009999999993261476183254832158476532184532858632649999 9999999999999 9999999999999999999999999999999999977169267891725334585 2247504434951 6024604083677867120133343721921422849679050222504698158 2684861279654 6840498863383873805387096230571111779386748183286234597 9729718899223 868793839031484514844173097... appears to be much more interesting.

Reminds me of the book _Contact_ by Carl Sagan... if the two numbers were pi and e I'd be even more impressed.

What are you guys using to divide 155-digit numbers?

I used bc for the above division

|> 75.8326548321564532108210546328764321812865318732658742 1674213675984 |> 6321875999999000000000000000000000011111111110000000001 0000001000000 |> 0000100000010000000000100000010000000000100000010000000 0000000000000 |> 0009999999993261476183254832158476532184532858632649999 9999999999999 |> 9999999999999999999999999999999999977169267891725334585 2247504434951 |> 6024604083677867120133343721921422849679050222504698158 2684861279654 |> 6840498863383873805387096230571111779386748183286234597 9729718899223 |> 868793839031484514844173097... |> appears to be much more interesting.

What are you guys using to divide 155-digit numbers?

I use REXX, here is the four line program:

'Ted S.' schrieb:

I am using Scheme's built-in division, but the ancient version installed on this machine gives the result either in arbitrary-precision (as a fraction) or as a double, which is why I didn't see the regularity. Maybe the new version does, but I'm not booting the other machine now just to check.

I also assume that Python can do it out of the box.

Cheers

Can you tell me exactly what is so interesting about that quotient? What have you figured out from it?

Come on, Answer!

1174419192328135317274255658153198080427934304578038090 1680418304689456 6787292800844355644360850267694083886151344689499579001 3601143904693819 1548698505844910505316440847476718560478608108467963380 3451879461400354

I wanted to know if you got it solved right. So, what did you find?

1174419192328135317274255658153198080427934304578038090 1680418304689456 6787292800844355644360850267694083886151344689499579001 3601143904693819 1548698505844910505316440847476718560478608108467963380 3451879461400354

All I noticed is that there are dramatic paterns of 0's, 1's and 9's. I don't know how the numbers were constructed to achieve this.

Another thing I've noticed is that up until the first run of 9*[01]*9*, 0's and 1's are underrepresented: the frequency count is 0 1 2 3 4 5 6 7 8 9 2 9 11 9 7 9 9 7 10 1 In the next set between the sets of 9's, 0's and 9's are again underrepresented: 0 1 2 3 4 5 6 7 8 9 0 4 6 6 5 5 5 2 6 0 After the last set of 9's, the digit distribution evens out again.

I guess there could either be a cipher in there (monome-dinome?) or else this digit distribution is an artifact of whatever caused the strings of 9* and [01]*.

In short, no... I haven't solved it.