高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (979ﾚｽ)
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44: １３２人目の素数さん [sage] 2024/08/15(木) 10:18:26.54 ID:5ggTekS4

bWin <- function(x){# 1 beats 3, 3 beats 2, 2 beats 1
if(length(unique(x))!=2 ) return(0) # no winner
u=sort(unique(x))
if(all(u==c(1,2))) return(sum(x==2)) # how many winners who won by 2
if(all(u==c(2,3))) return(sum(x==3)) # how many winners who won by 3
if(all(u==c(1,3))) return(sum(x==1)) # how many winners who won by 1
}

janken.till.winner.sim <- function(n){ # janken till someone wins
if(n<2) return(NA)
x=sample(1:3,n,replace = TRUE) # janken by n people
count=1 # counter of janken game
while(bWin(x)==0){ # if draw try again
x=sample(1:3,n,replace = TRUE) # janken again till someone win
count=count+1
}
c(bWin(x),count) # return how many winners and counter
}

janken.till.chamipion.sim <- \(n){
re=janken.till.winner.sim(n)
count=re[2]
winner=re[1]
while(winner>1){
re=janken.till.winner.sim(n)
count=count+re[2]
winner=re[1]
}
count
}
res=replicate(1e5,janken.till.chamipion.sim(9))
summary(res)
hist(res,col=2,breaks='scott',freq=FALSE,xlab='count',main='')
BEST::plotPost(res,showMode = TRUE,breaks='scott')

http://rio2016.5ch.net/test/read.cgi/math/1723152147/44

763: １３２人目の素数さん [sage] 2025/03/25(火) 12:07:55.54 ID:JvJVqzfB

"
赤玉4個、黒玉3個、白玉2個、青玉1個を空箱なしで3つの箱にいれる。
箱を区別しないとき、入れ方は何通りあるか？
"
rm(list=ls())
# vector から remove　を除いた残りを返す
fn_rest <- function(vector,remove) Reduce(function(x, y) x[-match(y, x)], remove, init = vector)
fn_rest(c(1,2,2,3,3,3),c(2,3,3))

library(RcppAlgos)
v=rep(1:4,4:1)
pa=partitionsGeneral(10,3,repetition=TRUE) ; pa

pa[1,] # 1 1 8
c1=unique(comboGeneral(v,2)) ; c1
matrix(c("赤","黒","白","青")[c1],ncol=2) |> noquote()
re1=nrow(c1) ; re1

pa[2,] # 1 2 7
c2=unique(permuteGeneral(v,3)) ; c2
ans2=c2[apply(c2,1,\(x) x[2]<=x[3]),] ; ans2
matrix(c("赤","黒","白","青")[ans2],ncol=3) |> noquote()
re2=nrow(ans2) ; re2

pa[3,] # 1,3,6
c3=unique(permuteGeneral(v,4)) ; c3
ans3=unique(t(apply(c3,1,\(x) c(x[1],sort(x[2:4]))))) ; ans3
matrix(c("赤","黒","白","青")[ans3],ncol=4) |> noquote()
re3=nrow(ans3) ; re3

pa[4,] # 1 4,5
c4=unique(permuteGeneral(v,5)) ; c4
ans4=unique(t(apply(c4,1,\(x) c(x[1],sort(x[2:5]))))) ; ans4
matrix(c("赤","黒","白","青")[ans4],ncol=5) |> noquote()
re4=nrow(ans4) ; re4

pa[5,] # 2 2 6
c4=unique(comboGeneral(v,4)) ; c4
ans5=NULL
for(i in 1:nrow(c4)){
c22=c4[i,] ; c22
c2=unique(comboGeneral(c22,2)) ; c2
re22=cbind(c2,t(apply(c2,1, \(x) fn_rest(c22,x)))) ; re22
ans22=re22[apply(re22,1,\(x) sum(c(10,1)*x[1:2]) <= sum(c(10,1)*x[3:4])),] ; ans22
ans5=rbind(ans5,ans22)
}
matrix(c("赤","黒","白","青")[ans5],ncol=4) |> noquote()
re5=nrow(ans5) ; re5

pa[6,] # 2 3 5
c6=unique(permuteGeneral(v,5)) ; c6
ans6=unique(t(apply(c6,1,\(x) c(sort(x[1:2]),sort(x[3:5]))))) ; ans6
matrix(c("赤","黒","白","青")[ans6],ncol=5) |> noquote()
re6=nrow(ans6) ; re6

http://rio2016.5ch.net/test/read.cgi/math/1723152147/763

810: １３２人目の素数さん [sage] 2025/04/30(水) 08:07:51.54 ID:wedVH8wl

# Find data where the overall Fisher's exact test is not significant,
# but at least one pairwise Fisher's exact test (with Bonferroni correction) is significant.
res_no_overall_sig_pairwise_sig <- NULL
while (is.null(res_no_overall_sig_pairwise_sig) || res_no_overall_sig_pairwise_sig$fisher_pg > alpha || res_no_overall_sig_pairwise_sig$min_pairwise_p_bonf > alpha) {
res_no_overall_sig_pairwise_sig <- sim_fisher()
}
cat("Data where overall Fisher's test is not significant, but pairwise is:\n")
print(res_no_overall_sig_pairwise_sig)
cat("\n")

# Find data where the overall Fisher's exact test is significant,
# but all pairwise Fisher's exact tests (with Bonferroni correction) are not significant.
res_overall_sig_no_pairwise_sig <- NULL
while (is.null(res_overall_sig_no_pairwise_sig) || res_overall_sig_no_pairwise_sig$fisher_pg < alpha || res_overall_sig_no_pairwise_sig$min_pairwise_p_bonf < alpha) {
res_overall_sig_no_pairwise_sig <- sim_fisher()
}
cat("Data where overall Fisher's test is significant, but pairwise is not:\n")
print(res_overall_sig_no_pairwise_sig)

options(warn = 0)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/810

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