[This article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

1. Given a permutation of Ð, what is the probability that the most likely variation (up or down) occurs at each term?
2. Given three players choosing three different integers in Ð sequentially, and rewards in Ð allocated to the closest of the three players (with splits in case of equal distance), what is the reward for each given an optimal strategy?

For the first question, a simple code returns 0.17…

winofail<-function(permz){
if (length(permz)>1){
lenoperm=length(permz[-1])/2
win=(permzpermz)>lenoperm)+
(permz>permz)*(sum(permz[-1]lenoperm)+
(runif(1)<.5)*(sum(permz[-1]>permz)==lenoperm)
win=win&&winofail(permz[-1])
}else win=TRUE
return(win)}


(but the analytic solution exhibits a cool Pascal triangular relation!) and for the second question, a quick recursion or dynamic programming produces 20, 19, 15 as the rewards (and 5, 9, 8 as the locations)

gainz<-function(seqz){
difz=t(abs(outer(2:10,seqz,"-")))
cloz=apply(difz,2,rank)
return(apply(rbind(2:10,2:10,2:10)*
((cloz==1)+.5*(cloz==1.5)),1,sum))}

timeline<-function(prev){
if (length(prev)==0){
sol=timeline(10);bez=gainz(sol)
for (i in 2:9){
bol=timeline(i);comp=gainz(bol)
if (comp>bez){
bez=comp;sol=bol}}}
if (length(prev)==1){
bez=-10
for (i in (2:10)[-(prev-1)]){
bol=timeline(c(prev,i))
comp=gainz(bol)
if (comp>bez){
bez=comp;sol=bol}}}
if (length(prev)==2){
bez=-10
for (i in (2:10)[-(prev-1)]){
bol=c(prev,i)
comp=gainz(bol)
if (comp>bez){
bez=comp;sol=bol}}}
return(sol)}


After reading the solution on the Riddler, I realised I had misunderstood the line as starting at 2 when it was actually starting from 1. Correcting for this leads to the same 5, 9, 8 locations of picks, with rewards of 21, 19, 15.

To leave a comment for the author, please follow the link and comment on their blog: R – Xi'an's Og.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)

Click here to close (This popup will not appear again)