Oh wow, I really like the idea of turning gerrymandering into a puzzle! It reminds of puzzles like Nonograms, KenKen, and so on. And, it can teach you a thing or two about the real world's districting-patterns!
yeah, I love those types of puzzles! especially nonograms, those sorts of things are what especially inspired me to make this into a type of puzzle! it was just such a funny idea that I had to, and I ended up finding out a lot of really random interesting things through this rabbithole lol, including stuff about real life gerrymandering which I had no idea about
the text at 0:59 : "lmao imagine being a vice president of the United States, and what you're best known for is a corruprion term derived from your name. L bozo"
0:42 wikipedia - its intended pronunciation as named after Elbridge Gerry, is with a plosive [g] instead of the affricate [dʒ] which could appear so because of the front vowel [ɛ] following it
A couple years back my economics teacher literally assigned us a video game that you have to gerrymander to win. It was funny but actually pretty educational.
you kinda skipped over explaining why that puzzle can’t have more or less than 5 regions - with 50 regions of 1 or 1 region of 50, it’ll just be majority rule - with 25 regions of 2, the top left cell has no purple neighbors and therefore cannot be in an untied region - with 2 regions of 25, there aren’t enough purple cells to achieve a majority in both regions - with 10 regions of 5, 6 regions of 3 purple are required, with the remainder being entirely yellow. however, it is impossible for the cell in the bottom left to be in a region with 2 other purple cells
sounds like a fun competitive game where you have a big board of randomised coloured tiles and players competing to create the most districts in their colour, the bigger the more points. Though you would probably have to add another dimension so that it isn't a pure puzzle solving game.
During the section about the weird double minimas at 20:26, I noticed that each of the odd factors listed are 4x + 1 of the previous(or the next power of 4 + the previous number). so I did some testing and these were the results: number being tested factor, factor, smallest result of test (factors are only listed when they lead to the smallest result in testing) 16 1, 16, 36 4, 4, 36 320 5, 64, 396 16, 20, 396 5376 21, 256, 5676 64, 84, 5676 87040 272, 320, 88228 1396736 341, 4096, 1401516 1024, 1364, 1401516 22364160 4480, 4992, 22383108 357892096 5461, 65536, 357968556 16384, 21844, 357968556 5726535680 69904, 81920, 5726839332 91625619456 299008, 306432, 91626830340 1466014105600 1154560, 1269760, 1466018954244 23456242466816 1398101, 16777216, 23456262040236 4194304, 5592404, 23456262040236 375299946577920 19249152, 19496960, 375300024070148 6004799413682176 22369621, 268435456, 6004799726856876 67108864, 89478484, 6004799726856876 96076791692656640 304087040, 315951616, 96076792932733956 1537228671377473536 1228333056, 1251475456, 1537228676337090564 After this I was getting integer overflow errors. Its also worth noting that 87040 second smallest outcome is a double minima like the others. If i had to guess why this sort of works then I'd probably say that since it works for 16 if you were to time both factors by 4 but keep the odd one odd you might expect it to also work. Hope this helps.
This reminds me of a layton riddle wher you had to win a game of, I thinks it's called the war in english, but you have worse cards than your opponent so you have to follow the same strategy of just winning with a small advantage when you win and loosing by a lot when you loose
Not in this case. Gerrymandering is a separate problem, and won't be fixed by replacing FPTP with a better system. Gerrymandering _would_ be fixed by a switch to Proportional voting, but that's because switching to Proportional voting is specifically a change to the part of the political system that includes gerrymandering (it would replace the concept of "districts"). And it's quite possible to switch to Proportional voting without giving up FPTP; that's call "Party list PR".
87040 is also a 320-case: 85 * 2^10 = 340 * 2^8. More generally, (the sum from 0 to n of 4^n) * 4^(n+2) is the same as (4(the sum from 0 to n of 4^n)) * 4^(n+1)
@@tBagley43 Yes, that works, but it can be expressed with the explicit formula a(n) = 4^(n+1)*(sum from i=0 to (n-1) of 4^i), a(1) = 16, a(2) = 320, a(5) = 4^6 * (1+4+16+64+256) = 1396736.
@@rmrmarbleracing5372 oh yeah that's even easier, nice find. and actually you can express "sum from i = 0 to (n-1) of 4^i" more simply as "(4^n - 1)/3", so after distributing, the entire expression is: a(n) = (4^(2n+1) - 4^(n+1))/3. you could also reindex to make it a little nicer if you don't want to consider 0 as a trivial solution.
somebody beat me to it -- i was working on a simplified grid-based gerrymandering puzzle game too, ive been inactive in developing it for a while but i started a few months ago
It seems to me that a lot of the weird pattern shenanigans happen because of rounding up. I wonder if the pattern would be simpler if we said that for even numbers of districts and regions, getting a tie is equivalent to winning that region/board. Or in other words, if your goal was not to win, but to prevent the opponent from getting a strict majority.
17:45 I tried throwing those numbers into OEIS and it found just one sequence that goes 1,2,18,50,98,162,242,338,450,... Could you verify if your system also finds those additional numbers?
I was going to comment this if no one else did. I went right to the OEIS when he started talking about "random" sequences of numbers. Always worth checking that. Not sure how "Maximum number of regions into which the plane can be divided using n (concave) quadrilaterals." might connect to these puzzles but it could be worth looking at.
the tricolor puzzle at the end was fun, 3 sections with (3c 2m 2y), 2 sections with (0c 0m 7y), and 2 sections with (0c 4m 3y). I did manage to draw the arrangement too, but describing it in youtube comments doesn't seem efficient.
Looks like factors of the form 2k+2 have a strong tendency to have solutions that are k better than the norm. Does this continue for larger k, and for larger second factors, as well?
19:40 it sounds like 16 and 320 are forming their own sequence of numbers with their own switching factor of 4, which interleaves with the one you already found with switching factor of 2. At some point, you'll have to consider that you don't have an edge case but a perfectly formed separate sequence, especially since you didn't really explore that high (100's are tiny numbers by computational exploration standards) EDIT: nvm
Oh wow, I really like the idea of turning gerrymandering into a puzzle! It reminds of puzzles like Nonograms, KenKen, and so on. And, it can teach you a thing or two about the real world's districting-patterns!
RUclips legend located 🫵(I’m a fan)
🤜🤛
cary keeprigging houseofrepresentativeselections
It reminds me of games like minesweeper.
yeah, I love those types of puzzles! especially nonograms, those sorts of things are what especially inspired me to make this into a type of puzzle! it was just such a funny idea that I had to, and I ended up finding out a lot of really random interesting things through this rabbithole lol, including stuff about real life gerrymandering which I had no idea about
Gerrymandering was invented by Elbridge Gerry in 1812. That sounds like the Thomas Running joke, but it's actually real this time
Shrapnel was invented by John General Shrapnel
@@cubee4108 The German chocolate cake was invented by an English-American chocolate maker named Samuel German
Mewing was invented by doctor John mew
@@cubee4108 Henry but actually close. I can't tell if this is a joke or not sorry
@@m4rcyonstation93Henry but actually close was invented by close but actually henry
the text at 0:59 : "lmao imagine being a vice president of the United States, and what you're best known for is a corruprion term derived from your name. L bozo"
I actually love Gerrymandering puzzles. I’ve played two flash games where that’s the mechanic, and it’s really fun
there was a flash game called the redistricting game that I miss dearly
It might be on Flashpoint, have you checked?
I remember a mobile game with the same idea as this video too. The names of the levels were wild. If only it was still around
18:19, those numbers are all two times an odd perfect square. I’m not sure if that’s significant or not but I’d guess that it is.
0:42 wikipedia - its intended pronunciation as named after Elbridge Gerry, is with a plosive [g] instead of the affricate [dʒ] which could appear so because of the front vowel [ɛ] following it
It's not called garymandering
I believe everest is a similar situation
@@BookWyrmOnAStringyea George everest pronounced his name /ivrɪst/ but the modern pronunciation is (depending on your dialect) /ɛvrɪst/
list of all non-sequence numbers below 1 million:
16 - (1, 16), (4, 4) - 9 districts
320 - (5, 64), (16, 20) - 99 districts
784 - (16, 49), (28, 28) - 225 districts
3536 - (17, 208), (52, 68) - 945 districts
5376 - (21, 256), (64, 84) - 1419 districts
10208 - (29, 352), (88, 116) - 2655 districts
13376 - (64, 209), (88, 152) - 3465 districts
16576 - (37, 448), (112, 148) - 4275 districts
20336 - (41, 496), (124, 164) - 5229 districts
36848 - (112, 329), (188, 196) - 9405 districts
44896 - (61, 736), (184, 244) - 11439 districts
48256 - (128, 377), (208, 232) - 12285 districts
95408 - (89, 1072), (268, 356) - 24165 districts
113296 - (97, 1168), (292, 388) - 28665 districts
122816 - (101, 1216), (304, 404) - 31059 districts
143008 - (109, 1312), (328, 436) - 36135 districts
191744 - (256, 749), (428, 448) - 48375 districts
225776 - (137, 1648), (412, 548) - 56925 districts
267008 - (149, 1792), (448, 596) - 67275 districts
270256 - (304, 889), (508, 532) - 68085 districts
296416 - (157, 1888), (472, 628) - 74655 districts
343408 - (169, 2032), (508, 676) - 86445 districts
393856 - (181, 2176), (544, 724) - 99099 districts
398816 - (352, 1133), (484, 824) - 100359 districts
466496 - (197, 2368), (592, 788) - 117315 districts
525008 - (209, 2512), (628, 836) - 131985 districts
630208 - (229, 2752), (688, 916) - 158355 districts
697936 - (241, 2896), (724, 964) - 175329 districts
793616 - (257, 3088), (772, 1028) - 199305 districts
864416 - (544, 1589), (908, 952) - 217035 districts
869408 - (269, 3232), (808, 1076) - 218295 districts
921856 - (277, 3328), (832, 1108) - 231435 districts
948656 - (281, 3376), (844, 1124) - 238149 districts
784 is even weirder than 320 because (16,49) and (28,28) aren't even an (a,b)-(4a,b/4) pair
the numbers that don't form pairs like this are 784, 13376, 36848, 48256, 191744, 270256, 398816, 864416, 1082848, 1565120, 1581664, 2020928, 2762560, 2766368, 3060736, and 3981712
(28,28) does form an (a,b)-(4a,b/4) pair with (7,112), but that requires 228 minority districts, while (28,28) only requires 225 minority districts
What if we write these numbers in binary
A couple years back my economics teacher literally assigned us a video game that you have to gerrymander to win. It was funny but actually pretty educational.
4:13 Invalid solution! There's two V and T pentominoes- wait, this isn't pentomino pathfinding... anyway
3:35 now it’s Wario vs Waluigi.
Which is, to be fair, more important topic than any politics anywhere in the world.
I’m glad all Waluigi can win every single time, even with Wario’s popularity.
The Electoral Circus: The Game
you kinda skipped over explaining why that puzzle can’t have more or less than 5 regions
- with 50 regions of 1 or 1 region of 50, it’ll just be majority rule
- with 25 regions of 2, the top left cell has no purple neighbors and therefore cannot be in an untied region
- with 2 regions of 25, there aren’t enough purple cells to achieve a majority in both regions
- with 10 regions of 5, 6 regions of 3 purple are required, with the remainder being entirely yellow. however, it is impossible for the cell in the bottom left to be in a region with 2 other purple cells
I'd love to see Numberphile examine these weird cases. It sounds interesting
sounds like a fun competitive game where you have a big board of randomised coloured tiles and players competing to create the most districts in their colour, the bigger the more points. Though you would probably have to add another dimension so that it isn't a pure puzzle solving game.
John Gerrymander really cooked with this
Actually it was Elbridge Gerry
During the section about the weird double minimas at 20:26, I noticed that each of the odd factors listed are 4x + 1 of the previous(or the next power of 4 + the previous number). so I did some testing and these were the results:
number being tested
factor, factor, smallest result of test (factors are only listed when they lead to the smallest result in testing)
16
1, 16, 36
4, 4, 36
320
5, 64, 396
16, 20, 396
5376
21, 256, 5676
64, 84, 5676
87040
272, 320, 88228
1396736
341, 4096, 1401516
1024, 1364, 1401516
22364160
4480, 4992, 22383108
357892096
5461, 65536, 357968556
16384, 21844, 357968556
5726535680
69904, 81920, 5726839332
91625619456
299008, 306432, 91626830340
1466014105600
1154560, 1269760, 1466018954244
23456242466816
1398101, 16777216, 23456262040236
4194304, 5592404, 23456262040236
375299946577920
19249152, 19496960, 375300024070148
6004799413682176
22369621, 268435456, 6004799726856876
67108864, 89478484, 6004799726856876
96076791692656640
304087040, 315951616, 96076792932733956
1537228671377473536
1228333056, 1251475456, 1537228676337090564
After this I was getting integer overflow errors. Its also worth noting that 87040 second smallest outcome is a double minima like the others. If i had to guess why this sort of works then I'd probably say that since it works for 16 if you were to time both factors by 4 but keep the odd one odd you might expect it to also work. Hope this helps.
This video is NOT about the politics and nuances of REAL LIFE gerrymandering!
Took the words right out of my mouth (ew)
What title did it show you? The title I saw ("Let's turn America's broken election system into a puzzle genre!") seems honest to me.
This reminds me of a layton riddle wher you had to win a game of, I thinks it's called the war in english, but you have worse cards than your opponent so you have to follow the same strategy of just winning with a small advantage when you win and loosing by a lot when you loose
Yeah, all of these problems go back to First Past the Post… (CGP Grey)
Sadly, he's stuck on transferrable vote and applies that bias to his later videos.
@@tristanridley1601 As opposed to what?
Not in this case. Gerrymandering is a separate problem, and won't be fixed by replacing FPTP with a better system.
Gerrymandering _would_ be fixed by a switch to Proportional voting, but that's because switching to Proportional voting is specifically a change to the part of the political system that includes gerrymandering (it would replace the concept of "districts"). And it's quite possible to switch to Proportional voting without giving up FPTP; that's call "Party list PR".
I did this as an assignment in school once lol. We were given a map and were told to gerrymander it. It was fun!
87040 is also a 320-case: 85 * 2^10 = 340 * 2^8.
More generally, (the sum from 0 to n of 4^n) * 4^(n+2) is the same as (4(the sum from 0 to n of 4^n)) * 4^(n+1)
it looks like a recurrence relation:
a(0) = 0
a(1) = 16
a(n) = 20*a(n-1)-64*a(n-2)
so the next number ought to be 1396736, could you check that?
@@tBagley43 Yes, that works, but it can be expressed with the explicit formula a(n) = 4^(n+1)*(sum from i=0 to (n-1) of 4^i), a(1) = 16, a(2) = 320, a(5) = 4^6 * (1+4+16+64+256) = 1396736.
@@rmrmarbleracing5372 oh yeah that's even easier, nice find. and actually you can express "sum from i = 0 to (n-1) of 4^i" more simply as "(4^n - 1)/3", so after distributing, the entire expression is: a(n) = (4^(2n+1) - 4^(n+1))/3. you could also reindex to make it a little nicer if you don't want to consider 0 as a trivial solution.
21:32
Yeah, well what if instead of a bean stalk, we had a bean trellis?
somebody beat me to it --
i was working on a simplified grid-based gerrymandering puzzle game too, ive been inactive in developing it for a while but i started a few months ago
0:58 Elbridge Gerry was actually pronounced with a g, but due to the word gerrymander spreading people started mispronouncing it as a j.
It seems to me that a lot of the weird pattern shenanigans happen because of rounding up. I wonder if the pattern would be simpler if we said that for even numbers of districts and regions, getting a tie is equivalent to winning that region/board. Or in other words, if your goal was not to win, but to prevent the opponent from getting a strict majority.
17:45 I tried throwing those numbers into OEIS and it found just one sequence that goes 1,2,18,50,98,162,242,338,450,...
Could you verify if your system also finds those additional numbers?
that is 2*each odd perfect square except the 1 fsr (2 * 1², 2 * 3², 2 * 5², 2 * 7², …)
I was going to comment this if no one else did. I went right to the OEIS when he started talking about "random" sequences of numbers. Always worth checking that. Not sure how "Maximum number of regions into which the plane can be divided using n (concave) quadrilaterals." might connect to these puzzles but it could be worth looking at.
the tricolor puzzle at the end was fun, 3 sections with (3c 2m 2y), 2 sections with (0c 0m 7y), and 2 sections with (0c 4m 3y). I did manage to draw the arrangement too, but describing it in youtube comments doesn't seem efficient.
please turn this into an actual game!
BTW for the chapter feature to work I believe you need to have 0:00 also as a chapter
Don't let politicians play this game
this is some cracking the cryptic material
12:39, purple isn't the minority in either of these
6:14 this actually looks like the exact minimum number of purples!
3:31 I don't want to tie this colors to political parties *Proceeds to use the colors of the political parties of my country*
Looks like factors of the form 2k+2 have a strong tendency to have solutions that are k better than the norm. Does this continue for larger k, and for larger second factors, as well?
I never knew gerrymandering was a portmanteau
That puzzle was fun!
gerrymeowering
Wait this isnt I see le puzzles channel
WHY IS YOUR VOICE SO SIMILAR TO CARY KH
the grid you made for the minimum cells to win looks like how minecraft tnt works when its explosion size gets really big.
20:33 shouldn’t the bottom right power of two be 2^6?
What font do you use for your visualizations?
Do the 3-colored ones follow majority-rule or first past the post?
19:40 it sounds like 16 and 320 are forming their own sequence of numbers with their own switching factor of 4, which interleaves with the one you already found with switching factor of 2. At some point, you'll have to consider that you don't have an edge case but a perfectly formed separate sequence, especially since you didn't really explore that high (100's are tiny numbers by computational exploration standards)
EDIT: nvm
Or you could use Proportional Representation.
3:22 i think the labels are wrong?
I would like to code this puzzle game, can I?
But what if
the minorities were pentominos
lets go america
Making this game looks fun, you could do it with graph theory, and a breath first search
2:49 Egg
Woah you sound just like carykh
Clever stuff
His name was actually Gerry where the g is pronounced like the g in great.
1 *4+1 = 5, 5 *4+1 = 21, and the multiplicand is 4^n, or OEIS A002450
Yay!
20:32, typo in the first line. It should end with 2^2 * 2^2 (not …2^4). Hope it helps. Great video!
it’s the same thing
Puzzles
Why US politics is fucked up: The Game
gerrymander? i hardly know her
Links a Map Men video he clearly didn't watch.
17 hours ago
7 hours ago
888 views, 8 hrs ago
Gerrymandering is innately political
Trying to make the game not political is a form of lying
I think he meant not associating the party he wants to win with a real world party
If people understand gerrymandering apolitically, it will make it harder to get away with politically.
f1rst!