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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