# seven digit addition

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**A**nother quick riddle from the riddler: solve the equation

EXMREEK + EHKREKK = ?K?H?X?E

which involves every digit between 0 and 9. While the puzzle can be unravelled by considering first E and K, which must be equal to 6 and 3, a simple R code also leads to the conclusion

isok <- function(a,b){ s=as.numeric(unlist(strsplit(as.character(sum(10^(6:0)*a)+ sum(10^(6:0)*b)),""))) if (length(s)==7){ goal=FALSE}else{ goal=(length(unique(c(a,b,s)))==10)&(a[2]==s[6])& (s[8]==a[6])&(s[2]==a[7])&(b[2]==s[4])} return(goal)} pasok <- function(T=1e3){ for (t in 1:T){ a[1]=a[5]=a[6]=6;a[7]=3 digs=sample(c(0:2,4,5,7:9),4) a[2:4]=digs[1:3] b[1]=a[1];b[2]=digs[4]; b[3]=a[7];b[4]=a[4];b[5]=a[1];b[6:7]=a[7] if (isok(a=a,b=b)) print(rbind(a,b))}} > pasok() [,1] [,2] [,3] [,4] [,5] [,6] [,7] a 6 2 4 7 6 6 3 b 6 8 3 7 6 3 3

which sum is 13085296.

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