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****T**he weekend riddle from The Riddler is rather straightforward [my wording and simplification]:

*Construct a decimal number X between 0 and 1 by drawing the first digit a¹ uniformly over {0,1,…,9}, the second digit a² uniformly over {0,1,…,9}, &tc., until 0 is attained. What is the expectation of this random variable X?*

Since each new digit has expectation half of the previous digit, the expectation is an infinite geometric series with common ratio 20⁻¹ and factor 9, leading to an expectation of 9/19. As verified with the following R code:

skr<-function(){ a=9;b=0 while((a<-sample(rep(0:a,2),1))>0)b=10*b+a while(b>=1)b=b/10 return(b)}

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