## Le Monde puzzle [#1133]

Posted in Books, Kids, R with tags , , , , , , on March 28, 2020 by xi'an A weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check):

If ADULE-ELUDA=POINT, was is the largest possible value of POINT? With the convention that all letters correspond to different digits and no digit can start with 0. Same question when ADULE+ELUDA=POINT.

The run of a brute force R search return 65934 as the solution (codegolf welcomed!)

```dify<-function(adule)
(sum(adule*10^(4:0))-sum(rev(adule)*10^(4:0)))
num2dig<-function(dif) (dif%/%10^(0:4))%%10
sl=NULL
for (t in 1:1e6){
adule=sample(0:9,5)
while((dify(adule)<=0)||(!prod(adule[c(1,5)])))
adule=sample(0:9,5)
point=rev(num2dig(dify(adule)))
if ((!sum(duplicated(point)))&(prod(point%in%(0:9)[-adule-1])))
sl=rbind(sl,c(adule,point))}
sl=as.matrix(distinct(as.data.frame(sl),.keep_all = TRUE))
```

where distinct is a dplyr R function.

```> 94581-18549
 76032
```

The code can be easily turned into solving the second question

```> 31782+28713
 60495
```