**A** weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check):

If ADULE-ELUDE=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+ELUDE=POINT.

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

dify<-function(aluda,point) (sum(aluda*10^(4:0))-sum(rev(aluda)*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(aluda)<=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 [1] 76032

The code can be easily turned into solving the second question

> 31782+28713 [1] 60495