# Le Monde puzzle [#7]

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The mathematical puzzle from the weekend edition of Le Monde from a few weeks ago was not too hard to solve by induction but my R code failed miserably! The puzzle was as follows:

A calculator is broken in such a way that it starts by exhibiting 0, then pressing 4, 6 or 0 keeps adding this figure to the right of the current number (if not zero), while pressing 2 divides the current number by 2. For instance, a possible sequence is0 4 [press 4] 46 [press 6] 23 [press 2] 230 [press 0]

Is it possible to exhibit any integer?

I thus wrote the simple R code

library(gsubfn) digitBase=function(n){ strapply(as.character(n), ".", as.numeric)[[1]] } check=function(x){ step=0 xdigits=digitBase(x) ok=sum(xdigits==0)+sum(xdigits==4)+sum(xdigits==6) if (ok<length(xdigits)){ y=2*x step=1+check(y) } step }

which unfortunately runs very quickly into problems as can be seen by calling

> check(7) Error in if (ok < length(xdigits)) { : missing value where TRUE/FALSE needed In addition: Warning messages: 1: In do.call(FUN, as.list(s[, j])) : NAs introduced by coercion 2: In do.call(FUN, as.list(s[, j])) : NAs introduced by coercion 3: In do.call(FUN, as.list(s[, j])) : NAs introduced by coercion

because the 2x…x2x7 value gets out of bounds…

Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle

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