Le Monde puzzle [#737 re-read]

As 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 (y₀,z₀,w₀)=(38,40,46) and…it does not work! The value of (x₁,y₁,z₁,w₁) is indeed (19,39,43,8.5). Now, it does not work because the 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 uⁿ=(x_n,y_n,z_n,w_n), for i=1,…,4,

$u_i^n=\frac{1}{2}\left(u_i^{n-1}+\min_{j;u_j^{n-1}>u_{i}^{n-1}}u_{j}^{n-1}\right)\,\text{mod}\,48$

if u_i^n-1 is not the maximum of u^n-1 and

$u_{i}^{n}=\frac{1}{2}\left(u_{i}^{n-1}+48+\min_{j\ne i}u_{j}^{n-1}\right)\,\text{mod}\,48$

otherwise.

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

[sourcecode language=”r” gutter=”false”]
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()}
}}
[/sourcecode]

This new version leads to solutions (unsurprisingly!), returning

[sourcecode gutter=”false”]
> print(start)
[1] 0 12 24 36
[/sourcecode]

as one solution in 8 steps and

[sourcecode gutter=”false”]
> print(start)
[1] 0 38 40 46
[/sourcecode]

as the quickest solution in 6 steps.

This entry was posted on August 27, 2011 at 11:11 am and is filed under R with tags Le Monde, mathematical puzzle. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “Le Monde puzzle [#737 re-read]”

3rd degree assessment of unemployment « Xi'an's Og Says:
September 4, 2011 at 4:04 am

[…] le Monde, a few days ago, the front page title was “l’augmentation du chômage […]

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Xi'an's Og