Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:57 PM
I've gained a lot of friends since I last put it forth so here's an old logic puzzle I like. don't spoil the answer if you know it
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:57 PM
Proposing a game with the following rules
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:57 PM
You start with the string "MI"
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:57 PM
then, you can perform four different translations on it
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:57 PM
1: For any string of the form Mx, you can replace it with Mxx, doubling everything after the M
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:58 PM
2: Anywhere in any string, "III" can be replaced with "U"
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:58 PM
3: If the string ends in an I, you can append a U to the end
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:58 PM
4: Any time "UU" appears in a string, it can be deleted
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:58 PM
Goal: From MI, create MU
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 1:58 PM
Or: Prove that it can't be done
ғᴏxʏᴍᴏʀᴏɴ
@lastbastion
Mon, Apr 3, 2023 1:59 PM
... hm
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:00 PM
Mon, Apr 3, 2023 2:00 PM
from the book Godel, Escher, Bach: An Eternal Golden Braid, which was DEEPLY formative for a young quinn
ғᴏxʏᴍᴏʀᴏɴ
@lastbastion
Mon, Apr 3, 2023 2:00 PM
I don't know if I've done this before
I have a couple of ideas but I will not say anything in case I have
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:00 PM
you could rot13 it
ғᴏxʏᴍᴏʀᴏɴ
@lastbastion
Mon, Apr 3, 2023 2:01 PM
rot13 is a pain in the ass on mobile
I'll wait for someone else to get it then post my thing
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:01 PM
If I have MIU
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:01 PM
and I double it
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:02 PM
That would turn into MIUIU right?
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:02 PM
MIUIU, yep
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:02 PM
If I doubled it again and got MIUIUIUIU could I turn the Is into a U or do the Is have to be in a row?
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:02 PM
they must be in a row
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:02 PM
Mon, Apr 3, 2023 2:02 PM
the exact substring III
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:02 PM
ok
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:03 PM
This doesn't FEEL possible
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:04 PM
Because you need to get the Is to be a multiple of 3
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:04 PM
which you can't do by just doubling, I don't think
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:04 PM
that is correct! well observed/intuited
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:04 PM
oh that's just it
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:05 PM
doubling will never add a 3 to a number's factors
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:05 PM
and 1 is not divisible by 3
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:05 PM
therefore it's impossible to root out all the I's
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:05 PM
I was sure there was some kind of clever solution
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:05 PM
nope it's just impossible
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:05 PM
that took me much longer to figure out when I was like 14
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:06 PM
and of course, if a number isn't divisible by 3, then subtracting 3 also won't make it divisible by 3
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:06 PM
so the III -> U rule doesn't get you any closer either
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 2:06 PM
and the other two rules don't interact with the I count
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 2:18 PM
The only point I wasn't sure on was "what if there's a power of 2 somewhere that is also a multiple of 3?"
ғᴏxʏᴍᴏʀᴏɴ
@lastbastion
Mon, Apr 3, 2023 4:10 PM
see my answer was
I thought it was a language pun
you cannot create nothingness (無)
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:11 PM
here's the secret
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:11 PM
it literally is
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:11 PM
like that's why Hofstadter chose M and U for two of the symbols
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:12 PM
your read was correct
ғᴏxʏᴍᴏʀᴏɴ
@lastbastion
Mon, Apr 3, 2023 4:12 PM
ha
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:12 PM
everything in GEB is always operating on multiple levels
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 4:15 PM
the thing I think about the most from that was God Over Djinn
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:16 PM
hell yes
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:16 PM
or more specifically
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 4:16 PM
G.O.D Over Djinn
Gabiluzbad
@Overbringer
Mon, Apr 3, 2023 4:17 PM
The transmission time approaches zero and the message reaches the top of the infinite tower
Lightning Bolt
@graygriffin
Mon, Apr 3, 2023 5:46 PM
i need to actually read this book someday
Quinneapolis
@quinn2win
Mon, Apr 3, 2023 5:47 PM
it's very important to me
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