Competition Problem Corpus Analysis: Windmill Depth, No Single Hardest Theorem — E8 Intelligence Research

{"FINDING:":[0],"The":[1,140],"corpus":[2],"spans":[3],"competition":[4],"problems":[5],"(Putnam,":[6],"IMO,":[7],"Collatz,":[8],"100":[9,90],"Prisoners)":[10],"but":[11],"yields":[12],"no":[13,86,131],"single":[14],"\\"hardest\\"":[15],"theorem;":[16],"the":[17,23,28,59,68,136,154],"deepest":[18],"structural":[19],"content":[20],"is":[21,113],"in":[22,43],"IMO":[24],"windmill":[25,141],"problem":[26,36,120],"and":[27],"MATH":[29],"dataset's":[30],"combinatorial":[31],"breadth.":[32],"|":[33,138],"MATH:":[34],"Windmill":[35],"(IMO":[37],"2011":[38],"Q2):":[39],"given":[40],"\\\\(n\\\\)":[41,81,99],"points":[42],"general":[44],"position,":[45],"a":[46,50,95,125],"rotating":[47],"line":[48,69],"through":[49],"pivot":[51,57],"point":[52],"\\\\(P\\\\)":[53],"sweeps":[54],"points,":[55],"switching":[56],"to":[58,71],"newly":[60],"passed":[61],"point;":[62],"prove":[63],"for":[64,111],"any":[65],"initial":[66,73],"pivot,":[67],"returns":[70],"its":[72],"orientation":[74],"after":[75],"\\\\(O(n^2)\\\\)":[76],"switches.":[77],"Collatz:":[78],"\\\\(f(n)=n/2\\\\)":[79],"if":[80,84],"even,":[82],"\\\\(3n+1\\\\)":[83],"odd;":[85],"closed-form":[87],"invariant":[88,129],"known.":[89],"Prisoners:":[91],"cycle":[92,106],"decomposition":[93],"of":[94,98,153],"random":[96],"permutation":[97],"elements;":[100],"success":[101],"probability":[102,104],"=":[103],"largest":[105],"length":[107],"\\\\(\\\\le":[108],"n/2\\\\),":[109],"which":[110],"\\\\(n=100\\\\)":[112],"\\\\(\\\\approx":[114],"1-\\\\ln":[115],"2":[116],"\\\\approx":[117],"0.30685\\\\).":[118],"Putnam":[119],"(from":[121],"video):":[122],"typically":[123],"involves":[124],"clever":[126],"bijection":[127],"or":[128],"—":[130],"specific":[132],"equation":[133],"extracted":[134],"from":[135],"summary.":[137],"CONNECTION:":[139],"problem's":[142],"pivot-switching":[143],"dynamics":[144],"Author:":[145],"Andrew":[146],"Stewart":[147],"Caldin,":[148],"Independent":[149],"Researcher,":[150],"UK.":[151],"Part":[152],"E8":[155],"Intelligence":[156],"Research":[157],"series.":[158],"Platform:":[159],"e8intelligence.com":[160]}