**A**s a coincidence, while I was waiting for the solution to puzzle #737 published this Friday in *Le Monde*, the delivery (wo)man forgot to include the weekend magazine and I had to buy it this morning with my baguette *(as if anyone cares!)*. The solution is *(y*_{0},z_{0},w_{0})=(38,40,46) and…it does not work! The value of* (x*_{1},y_{1},z_{1},w_{1}) is indeed *(19,39,43,8.5)*. Now, it does not work because t*he update mechanism used by the writers of the **Le Monde* column is to move all positions simultaneously, rather than one at a time: the update thus reads as

if *u*^{n}=(x_{n},y_{n},z_{n},w_{n}), for* i=1,…,4,*

if *u*_{i}^{n-1} is not the maximum of *u*^{n-1} and

otherwise.

(to compare with my earlier proposal). In this new configuration, the core of the R code I use is

while (nodd){
nsuite=suite=start=c(0,sort(2*sample(1:23,3)))
for (t in 1:20){
#some values of start never produce non-integer values
#of suite and never visit suite[1]=0
nsuite[-4]=(suite[-4]+suite[-1]+48*(suite[-1]-suite[-4]<0))/2
nsuite[4]=(suite[4]+suite[1]+48*(suite[1]-suite[4]<0))/2
suite=nsuite%%48
if ((suite[1]==0)||(max(is.decimal(suite))==1)){
nodd=(max(is.decimal(suite))==1)
print(t)
break()}
}}

**T**his new version leads to solutions (unsurprisingly!), returning

> print(start)
[1] 0 12 24 36

as one solution in 8 steps and

> print(start)
[1] 0 38 40 46

as the quickest solution in 6 steps.

Filed under: R Tagged: Le Monde, mathematical puzzle

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**Tags:** Le Monde, mathematical puzzle, R