#Two functions that can be used to simulate the following game:
#(1) we place 4 coins on a table, (2) we choose a number k at random
#from the set 1:5, (3) if we choose k=5 we do nothing, but otherwise
#we turn over coin k. We then repeat this process 10 times.


chooseandturn<-function(v){
k<-sample(1:5,1,F,c(1/5,1/5,1/5,1/5,1/5));
if(k<5){v[k]<-(-1)*v[k]};
return(v)
}

getNafter10<-function(){
v<-c(1,1,1,1);
for(j in 1:10){v<-chooseandturn(v)};
return(2+sum(v)/2)
}


#We can then use this code to find the distribution of N,
#the number of heads that one has from the 10-step process.