285:
Farnsworth finds that Amy's human body cannot take the thrills he is seeking out. Even as they give up, they find they cannot revert to their own bodies, because the device will not operate on the same pairing of bodies. The
Professor first suggests they might be able to switch back to their original bodies with a third person. Bender volunteers and switches bodies with the Professor (in Amy's body) so he can perform a robbery without being identified. As Bender rushes out, the Professor realises that the three of them still will not be back in their real bodies, so he decides to run away in Bender's body and join the Robot Circus, renaming himself Nonchalanto and performing foolhardy stunts for cheap thrills.
340:, Ethan "Bubblegum" Tate and "Sweet" Clyde Dixon, mathematically prove that everyone's minds can be restored using two additional bodies. They proceed to do so, using themselves as the extras. Hermes reveals that Amy's temporary fast put her off her food long enough for him to shed some weight and Amy has been cured of her desire to binge-eat, while the Professor has gotten some of the thrills out of his system and learned that his old body is a memento of his life, not a punishment for his age. Realizing that common folk do not have such carefree lives as he had thought, Nikolai makes Clyde a Duke, and as he leaves, Bender realizes that the real crown is still in
289:
Bender states that he is really a robot who has switched bodies with a human, Nikolai reveals that he feels trapped by his wealth and wishes to live the life of a normal, "peasant" robot for a while. With Bender unable to find his real body, he tricks him into switching bodies with the robot
Washbucket and inhabits Nikolai's body, planning to live the life of an Emperor. Washbucket, now in Amy's body, professes
333:. Watching from the Robot Circus, the Professor realizes what is going on, but the only way to get there in time would be by Big Bertha's cannon. He is hesitant because this would end her life, but as a loyal Robo-Hungarian she insists, and Bender is saved with the assistance of the Professor - and the circus' twenty loyal Robo-Hungarian robot clowns who travel in his chest compartment.
1329:", writing, "Really, this is pure silly from beginning to end, using the show's internal logic to arrive in unpredictable places, and bringing to life a piece of fan fiction I doubt anyone has ever had the courage to write. It reminded me more than a little of 'The Farnsworth Parabox': a premise that uses the whole cast to just the right amount." Merrill Barr of
833:
1348:
plot offers up a level of complexity rarely offered by sitcoms, or any episodic television. 'The
Prisoner of Benda' was a perfect example of how Futurama takes an extremely simple concept and executes it in a daring and unique way. It's not as showy as 'A Clockwork Origin' or 'The Late Philip J. Fry'
320:
in an attempt to repulse Leela. During this time, Amy's constant appetite makes Leela's body become massively fat until Hermes switches bodies with her because she cannot make his body much worse. However while at the restaurant Amy (as Hermes) witnesses Fry and Leela on their repulsive date, putting
219:
build a machine that allows them to switch minds so that they may each pursue their lifelong dreams. However, they learn that the machine cannot be used twice on the same pairing of bodies. To try to return to their rightful bodies, they involve the rest of the crew in the mind switches, leaving each
1335:
also gave the episode a positive review, praising the character development of
Scruffy the Janitor in particular. With respect to the logic puzzle nature of the plot, Barr stated, "I have never understood less of what was going on in a single episode of Futurama. And I couldn't have loved it more."
288:
Bender — now in Amy's body — goes aboard
Nikolai's yacht, planning to steal his crown. He knocks out Nikolai's first officer and cousin. After binding and gagging him, he realizes his timing is off and accidentally throws his watch through a metal detector. He is then captured by the Emperor. When
300:
At the circus, the
Professor is having a fine time as the world's most indifferent robot daredevil, when he meets the Grande Dame, the robot cannon Big Bertha. He politely asks if he could be shot from her, but she admits that she is so old, it would end her life. He asks if she would like a new,
284:
using a new invention so that he can relive his youth. Likewise, Amy longs for her younger days of constantly eating and wishes to use the
Professor's skinny body to gorge herself with food for a while. However Amy finds that the Professor's aging body simply cannot digest like it used to, while
1363:
critic Alex Zalben concluded that "this season of
Futurama, despite a miss or two, has hit what might possibly be a series high for the past few episodes, and I can't wait to watch the rest. Kudos to Comedy Central for bringing back what is now officially the best animated show on TV." Alasdair
408:
scenario in which no pair of bodies can swap minds more than once. The proof demonstrates that after any sequence of mind switches, each mind can be returned to its original body by using two additional individuals who have not yet swapped minds with anyone. A formal statement is as follows:
643:
1201:
324:
In the meantime, Zoidberg and
Nikolai, in the respective bodies of Fry and Washbucket, become friends and attempt to assume the lives of Fry and Bender. Zoidberg is completely unused to normal living conditions however, and blows up Bender's apartment.
328:
Back on the yacht, Nikolai's cousin and fiancee reveal to Bender that they have been having an affair, and are planning to kill him and blame the burglar. Even learning he is actually Bender does not change their minds. They chase him to the
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and directed by
Stephen Sandoval and was met with acclaim from critics. The issue of how each crew member can be restored to their correct body given the limitation of the switching device is solved in the episode by what
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1376:" even coming close. 'The Prisoner of Benda' easily could have stretched out to a 70-minute DVD movie, but I'm just as happy to see it as 22 minutes of finely concentrated crazy." In an interview,
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371:, and then used it to explain the plot twist in this episode. However, Keeler does not feel it carries enough importance to be designated a theorem, and prefers to call it a
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her off her food. Trying to one-up each other, Fry and Leela end up having sex with each other in their equally grotesque bodies, and they admit they actually enjoyed it.
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from an animation standpoint, but with writing this tight we could be watching stick figures at 8 frames a second and it would still be worth seeing." Robert Canning of
828:{\displaystyle \pi ^{*}={\begin{pmatrix}1&2&...&k&k+1&...&n&x&y\\2&3&...&1&k+1&...&n&x&y\end{pmatrix}}.}
1300:
on August 19, 2010. In its original American broadcast, "The Prisoner of Benda" received 1.774 million viewers, down nearly 150,000 from the previous week's episode, "
394:
In a 2012 interview, David X. Cohen said that this was probably the first time that a mathematical theorem was proven in a television script, and that it was probably
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gave the episode a 9.5/10, stating "'The Prisoner of Benda' was an absolutely stellar episode. The high-concept idea of switching minds/bodies was taking [
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member free to pursue their own personal endeavors in a different crew member's body. The episode is composed of multiple subplots, with the main subplot being
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young body, but she turns him down briskly, telling him that her body may be old, but it is still hers to treasure, giving him pause for thought.
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switches bodies with Amy, thus inhabiting the Professor's body. Of course Fry is disgusted, and then upset when she claims to be right. He asks
297:, and even suggests they run away together, but he sadly turns her away, reminding her that he is still a man and she is janitorial equipment.
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638:{\displaystyle \pi ={\begin{pmatrix}1&2&...&k&k+1&...&n\\2&3&...&1&k+1&...&n\end{pmatrix}}.}
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be an arbitrary permutation on . It consists of disjoint (nontrivial) cycles and each can be inverted as above in sequence after which
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1196:{\displaystyle \pi ^{*}\sigma ={\begin{pmatrix}1&2&...&n&x&y\\1&2&...&n&y&x\end{pmatrix}}.}
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The episode was unanimously acclaimed by critics, who largely praised the episode's complexity and writing. Ken Keeler won a
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rated the episode 9.1/10. He praised the intricate plot and writing, also comparing it to "The Farnsworth Parabox" and "
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gave the episode a positive review, rating it an A−. Handlen compared the episode favorably to the season 4 episode "
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also praised the episode's mathematical complexity, saying "This episode is maybe the most epically overstuffed
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1359:] to extremes and delivered fantastic lines and great laughs throughout." In response to this episode
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and a 0.8 rating/2% share in the 18–49 demographic, down two tenths of a point from the previous week.
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1274:(a philosophical test designed to assess whether a computer can demonstrate true intelligence), actor
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for advice, who suggests he play Leela at her own game. Fry switches bodies with the disgusting alien
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Note that these are distinct transpositions, each of which exchanges an element of with one of
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1061:{\displaystyle \sigma =(x~~1)(x~~2)\cdots (x~~i)(y~~i+1)(y~~i+2)\cdots (y~~k)(x~~i+1)(y~~1).}
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The proof appears on the blackboard in the episode. The proof reduces to treating individual
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attempting to steal a crown, but ending up switching places with the Robo-Hungarian emperor.
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1675:"More Thursday Cable: 'Project Runaway' Up; Futurama, Real Housewives of DC Fall + More"
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The episode's title and the Robo-Hungarian emperor subplot are references to the 1894
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in Mathematics. The title and the story's main subplot is a reference to the 1894
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voices a desire to steal his crown, but no one is willing to be his accomplice.
261:. Series writer Eric Rogers considers this his favorite episode of the season.
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compartment. Having learned nothing, he begins plotting to re-steal the crown.
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can be reduced to the identity permutation by applying a sequence of distinct
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1804:"Futurama's mind-switching mayhem gives us the most depraved sex scene ever"
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writer Eric Rogers stated that this was his favorite episode of the season.
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Futurama volume 5 DVD commentary for the episode "The Prisoner of Benda"
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1496:"Futurama: Interview mit David X. Cohen, dem Co-Schöpfer der Serie"
1466:"Video: I once made this video about Futurama and Keeler's Theorem"
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Writers Guild of America Award for Outstanding Writing in Animation
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The episode begins with Emperor Nikolai of Robo-Hungary visiting.
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episode ever, with only the intersecting ensemble piece "
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Writers Guild of America Award for Television: Animation
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Keeler's theorem and products of distinct transpositions
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1593:"Futurama Review: "The Prisoner of Benda" (6.10)"
387:Theorem", while mathematician James Grime of the
1319:for his script to this episode. Zack Handlen of
1262:, in which a king is replaced by a commoner, by
2908:Cultural depictions of the Harlem Globetrotters
449:}, each of which includes at least one of
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1969:
1949:The Infosphere's take on the Futurama theorem
1586:
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1582:
1580:
8:
1304:". It received a 1.2 rating/2% share in the
1296:"The Prisoner of Benda" originally aired on
236:described in an interview as a mathematical
1879:"Futurama Preview: "The Prisoner of Benda""
308:may only be attracted to her for her body,
201:of the American animated television series
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1773:"Futurama: "The Prisoner of Benda" Review"
1708:"Review: Futurama — The Prisoner of Benda"
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1626:"Futurama - "The Prisoner of Benda" Recap"
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1344:", writing, "...this sort of intertwined,
425:be distinct objects that do not belong to
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27:10th episode of the 6th season of Futurama
2923:Television episodes written by Ken Keeler
1102:
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379:, an educational math website created by
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367:, penned and proved a theorem based on
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1739:"'Futurama' - 'The Prisoner of Benda'"
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1802:Wilkins, Alasdair (August 20, 2010).
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211:on August 19, 2010. In the episode,
7:
1737:Gallagher, Danny (August 20, 2010).
1317:63rd Writers Guild of America Awards
862:be the permutation obtained as the (
383:, refers to Keeler's result as the "
1771:Canning, Robert (August 20, 2010).
1673:Seidman, Robert (August 20, 2010).
1558:"Futurama: "The Prisoner Of Benda""
1270:. The episode also references the
170:
136:
1523:"Futurama - The Prisoner of Benda"
1214:-cycle to the identity and leaves
25:
2903:2010 American television episodes
1854:"CGEF Interview with Eric Rogers"
1706:Barr, Merrill (August 19, 2010).
1591:Gandert, Sean (August 20, 2010).
1556:Handlen, Zack (August 19, 2010).
1241:can be switched if necessary via
356:revealed that the episode writer
2147:The Futurama Holiday Spectacular
1624:Zalben, Alex (August 20, 2010).
1453:The Guardian-James Grime profile
401:s proudest mathematical moment.
1438:The Futurama Theorem and Puzzle
1278:, and the television character
331:United Nations General Assembly
194:" is the tenth episode in the
2133:Lrrreconcilable Ndndifferences
1342:Teenage Mutant Leela's Hurdles
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648:Introduce the two new symbols
161:Lrrreconcilable Ndndifferences
53:
1:
1919:Infosphere, the Futurama Wiki
1464:Grime, James (May 2, 2012).
1222:switched (without performing
391:calls it "Keeler's Theorem".
2365:Kill Gil, Volumes I & II
280:switches consciousness with
240:proved by Keeler, who has a
2918:Fiction about body swapping
2557:– "Xerox of a Xerox" (2020)
2444:Ned 'n' Edna's Blend Agenda
2317:The Dad Who Knew Too Little
227:The episode was written by
2939:
2913:Futurama season 6 episodes
2689:The Heart of Princess Osra
1657:"Big Bertha | weapon"
1521:Fabien (August 20, 2010).
1400:. American Physics Society
1075:. By routine verification:
492:Without loss of generality
404:The episode is based on a
2596:
2548:
2409:
2294:
2217:All the Presidents' Heads
2154:The Silence of the Clamps
2140:The Mutants Are Revolting
1996:
1858:Can't Get Enough Futurama
1502:. May 27, 2012. p. 4
1398:"Profiles in Versatility"
417:be a finite set, and let
304:Meanwhile, insecure that
181:
171:
137:
128:
105:
94:August 19, 2010
41:
2583:Carl Carlson Rides Again
2077:Attack of the Killer App
1422:(DVD). 20th Century Fox.
2182:The Tip of the Zoidberg
1925:"The Prisoner of Benda"
1292:Broadcast and reception
389:University of Cambridge
2528:Thanksgiving of Horror
2105:The Late Philip J. Fry
1374:Three Hundred Big Boys
1327:The Farnsworth Parabox
1197:
1062:
829:
639:
470:separately, since all
2875:The Prisoner of Benda
2811:The Prisoner of Zenda
2786:The Prisoner of Zenda
2762:The Prisoner of Zenda
2754:The Prisoner of Zenda
2738:The Prisoner of Zenda
2722:The Prisoner of Zenda
2714:The Prisoner of Zenda
2682:The Prisoner of Zenda
2665:The Prisoner of Zenda
2420:The Prisoner of Benda
2189:Ghost in the Machines
2126:The Prisoner of Benda
1934:"A Prisoner of Benda"
1915:The Prisoner of Benda
1418:Cohen, David (2010).
1259:The Prisoner of Zenda
1210:reverts the original
1198:
1063:
830:
640:
478:cycles. So first let
429:. Any permutation of
352:In a 2010 interview,
250:The Prisoner of Zenda
192:The Prisoner of Benda
35:The Prisoner of Benda
18:Robo-Hungarian Empire
2827:Prem Ratan Dhan Payo
2797:(1963 stage musical)
2456:A Test Before Trying
2389:Wedding for Disaster
2329:Catch 'em if You Can
2084:Proposition Infinity
1943:The Futurama Theorem
1083:
878:
856:i ∈ {1 ... k-1
664:
501:
441: ∪ {
278:Professor Farnsworth
213:Professor Farnsworth
2877:" (2010 episode of
2565:– "Planteau" (2021)
2070:In-A-Gadda-Da-Leela
1712:Film School Rejects
1332:Film School Rejects
1249:Cultural references
381:Alexander Bogomolny
124:stays in Cygnus X-1
2573:– "Rectify" (2022)
2210:Fry Am the Egg Man
2119:A Clockwork Origin
2091:The Duh-Vinci Code
1638:on August 23, 2010
1396:Levine, Alaina G.
1302:A Clockwork Origin
1245:, as was desired.
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1184:
1058:
846:that interchanges
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816:
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149:A Clockwork Origin
133:Episode chronology
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2889:
2819:Prisoner of Zenda
2802:Rupert of Hentzau
2770:Rupert of Hentzau
2746:Rupert of Hentzau
2730:Rupert of Hentzau
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2098:Lethal Inspection
1887:. August 18, 2010
1631:UGO Entertainment
1361:UGO Entertainment
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1306:Nielsen ratings
1294:
1255:adventure novel
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839:
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267:
246:adventure novel
158:
146:
116:Opening caption
97:
95:
83:Production code
59:
28:
23:
22:
15:
12:
11:
5:
2936:
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2895:
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2888:
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2863:
2855:
2851:The Great Race
2847:
2841:
2839:
2835:
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2832:
2831:
2823:
2815:
2807:
2798:
2790:
2789:(1961 TV play)
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2377:Apocalypse Cow
2368:
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2341:Mommie Beerest
2332:
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2203:Yo Leela Leela
2199:
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2168:Law and Oracle
2164:
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2016:
2011:
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1983:
1981:
1980:
1973:
1966:
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1903:External links
1901:
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1679:TVbythenumbers
1662:
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1298:Comedy Central
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435:transpositions
354:David X. Cohen
349:
346:
266:
263:
234:David X. Cohen
209:Comedy Central
186:
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2780:
2779:
2778:Jhinder Bondi
2775:
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2640:
2635:
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2605:
2603:
2602:Complete list
2600:
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2579:
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2567:
2564:
2563:
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2500:
2496:
2493:
2489:
2488:
2484:
2481:
2477:
2476:
2475:Bob's Burgers
2472:
2469:
2468:Brick Like Me
2465:
2464:
2460:
2457:
2453:
2452:
2448:
2445:
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2256:
2255:
2252:
2239:
2238:Reincarnation
2235:
2232:
2231:Overclockwise
2228:
2225:
2224:Cold Warriors
2221:
2218:
2214:
2211:
2207:
2204:
2200:
2197:
2193:
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2020:
2017:
2015:
2012:
2010:
2007:
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2002:
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1998:
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1991:
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1886:
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1859:
1855:
1849:
1846:
1835:on 2013-01-17
1834:
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1780:
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1717:
1713:
1709:
1702:
1700:
1696:
1685:on 2012-10-13
1684:
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1612:
1600:
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1587:
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1581:
1577:
1565:
1564:
1563:The A.V. Club
1559:
1552:
1550:
1548:
1544:
1533:on 2010-08-21
1532:
1528:
1524:
1517:
1514:
1501:
1497:
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1483:
1471:
1467:
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1362:
1358:
1357:
1352:
1347:
1343:
1339:
1334:
1333:
1328:
1324:
1323:
1322:The A.V. Club
1318:
1314:
1309:
1307:
1303:
1299:
1291:
1289:
1287:
1283:
1281:
1277:
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1123:
1120:
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1110:
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1040:
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1016:
1007:
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992:
986:
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980:
971:
962:
959:
956:
947:
938:
929:
923:
917:
908:
899:
890:
884:
881:
874:
873:
872:
869:
865:
864:left to right
845:
844:transposition
822:
817:
811:
806:
801:
796:
793:
790:
785:
782:
779:
774:
769:
766:
763:
758:
753:
746:
741:
736:
731:
728:
725:
720:
717:
714:
709:
704:
701:
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693:
688:
682:
677:
672:
668:
660:
659:
658:
632:
627:
621:
616:
613:
610:
605:
602:
599:
594:
589:
586:
583:
578:
573:
566:
561:
558:
555:
550:
547:
544:
539:
534:
531:
528:
523:
518:
512:
507:
504:
497:
496:
495:
493:
477:
473:
469:
461:
456:
452:
448:
444:
440:
436:
432:
428:
424:
420:
416:
412:
411:
410:
407:
402:
397:
392:
390:
386:
382:
378:
374:
370:
366:
365:mathematician
363:
359:
355:
347:
345:
343:
339:
338:Globetrotters
336:Finally, two
334:
332:
326:
322:
319:
315:
314:Hermes Conrad
311:
307:
302:
298:
296:
292:
286:
283:
279:
274:
272:
264:
262:
260:
256:
252:
251:
247:
243:
239:
235:
230:
225:
223:
218:
214:
210:
206:
205:
200:
197:
193:
184:
180:
177:
175:
162:
156:
153:
150:
145:
141:
140:
131:
127:
123:
119:
117:
113:
108:
104:
93:
89:
85:
81:
78:
75:
71:
67:
63:
58:Season 6
57:
50:
46:
45:
40:
36:
31:
19:
2878:
2874:
2865:
2862:(1970 novel)
2857:
2849:
2825:
2818:
2810:
2801:
2792:
2784:
2776:
2768:
2761:
2753:
2745:
2737:
2729:
2721:
2713:
2694:
2687:
2680:
2663:
2660:Anthony Hope
2578:The Simpsons
2576:
2568:
2560:
2552:
2523:The Simpsons
2521:
2511:The Simpsons
2509:
2504:Time's Arrow
2497:
2485:
2473:
2463:The Simpsons
2461:
2451:The Simpsons
2449:
2439:The Simpsons
2437:
2427:The Simpsons
2425:
2419:
2413:
2384:The Simpsons
2382:
2372:The Simpsons
2370:
2360:The Simpsons
2358:
2348:The Simpsons
2346:
2336:The Simpsons
2334:
2324:The Simpsons
2322:
2312:The Simpsons
2310:
2298:
2125:
1984:
1918:
1891:February 15,
1889:. Retrieved
1882:
1873:
1862:. Retrieved
1857:
1848:
1837:. Retrieved
1833:the original
1829:"WGA Awards"
1823:
1813:February 15,
1811:. Retrieved
1807:
1784:February 15,
1782:. Retrieved
1776:
1753:February 15,
1751:. Retrieved
1747:the original
1742:
1732:
1722:February 15,
1720:. Retrieved
1716:the original
1711:
1687:. Retrieved
1683:the original
1678:
1651:
1640:. Retrieved
1636:the original
1629:
1604:February 15,
1602:. Retrieved
1596:
1569:February 15,
1567:. Retrieved
1561:
1535:. Retrieved
1531:the original
1526:
1516:
1504:. Retrieved
1499:
1490:
1480:– via
1476:February 15,
1474:. Retrieved
1459:
1448:
1442:Cut-the-Knot
1419:
1413:
1402:. Retrieved
1391:
1377:
1369:
1354:
1346:Altman-esque
1330:
1320:
1310:
1295:
1284:
1276:Nicolas Cage
1268:Anthony Hope
1257:
1252:
1228:
1205:
1070:
837:
656:, and write:
647:
486:-cycle on ={
472:permutations
465:
454:
450:
446:
442:
438:
430:
426:
422:
418:
414:
403:
395:
393:
384:
377:Cut-the-Knot
369:group theory
351:
341:
335:
327:
323:
303:
299:
290:
287:
275:
268:
259:Anthony Hope
248:
226:
202:
191:
189:
173:
154:
143:
42:
34:
2870:(1975 film)
2867:Royal Flash
2859:Royal Flash
2854:(1965 film)
2821:(1988 film)
2813:(1979 film)
2804:(TV series)
2764:(1952 film)
2756:(1937 film)
2748:(1923 film)
2740:(1922 film)
2732:(1915 film)
2724:(1915 film)
2716:(1913 film)
2706:Adaptations
2161:Möbius Dick
1860:. July 2010
1743:HuffPost TV
1364:Wilkins of
1272:Turing test
868:composition
854:. For any
348:The theorem
276:Meanwhile,
65:Directed by
2897:Categories
1864:2010-08-20
1839:2011-02-06
1689:2010-08-20
1642:2010-08-20
1537:2010-08-20
1404:2010-07-20
1384:References
1286:Big Bertha
1280:Fat Albert
1229:Next, let
358:Ken Keeler
229:Ken Keeler
174:Futurama
122:Cygnus X-1
98:2010-08-19
77:Ken Keeler
73:Written by
60:Episode 10
2845:Ruritania
2480:Housetrap
2305:Godfellas
2175:Benderama
1917:" at the
1527:Critictoo
1266:novelist
1206:That is,
1097:σ
1092:∗
1088:π
993:⋯
924:⋯
882:σ
842:) be the
673:∗
669:π
505:π
494:, write:
462:The proof
406:body swap
342:Nikolai's
257:novelist
2880:Futurama
2838:See also
2585:" (2023)
2530:" (2019)
2518:" (2018)
2506:" (2017)
2494:" (2016)
2482:" (2015)
2470:" (2014)
2458:" (2013)
2446:" (2012)
2434:" (2011)
2422:" (2010)
2415:Futurama
2391:" (2009)
2379:" (2008)
2367:" (2007)
2355:" (2006)
2343:" (2005)
2331:" (2004)
2319:" (2003)
2307:" (2002)
2300:Futurama
2196:Neutopia
2054:Season 6
1990:episodes
1986:Futurama
1378:Futurama
1370:Futurama
482:be some
476:disjoint
396:Futurama
385:Futurama
318:Zoidberg
293:love to
204:Futurama
176:season 6
144:Previous
52:Episode
44:Futurama
2063:Rebirth
2000:Seasons
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