## Le Monde puzzle [#1133]

**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 [1] 76032

The code can be easily turned into solving the second question

> 31782+28713 [1] 60495

April 30, 2020 at 3:10 pm

Hi Prof. Robert,

There might be some typos:

– in your question statement, `ELUDE` should be `ELUDA`,

– in your `dify` function, redundant `point` argument

– and `dify(aluda)` should be `dify(alude)` in the main code.

And you said the solution is 65934 before your code, but you return 76032 later.

I tried to make a slight modification, replacing `sample` with `for loop`, which seems shorter.

“`R

dify<-function(alude)

(sum(alude*10^(4:0))-sum(rev(alude)*10^(4:0)))

num2dig0)rev((dif%/%10^(0:4))%%10)else numeric(5)

sl=NULL

for (t in (1e5-1):1e4){

adule=num2dig(t)

if (!sum(duplicated(adule))){

point=num2dig(dify(adule))

if ((!sum(duplicated(point)))&&(prod(point%in%(0:9)[-adule-1])))

sl=rbind(sl,c(adule,point))}}

“`

April 30, 2020 at 9:37 pm

Thanks for the pointers.

March 29, 2020 at 8:15 am

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