Le Monde puzzle [#1094]
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A rather blah number Le Monde mathematical puzzle:
Find all integer multiples of 11111 with exactly one occurrence of each decimal digit..
Which I solved by brute force, by looking at the possible range of multiples (and borrowing stringr:str_count from Robin!)
> combien=0
> for (i in 90001:900008){
j=i*11111
combien=combien+(min(stringr::str_count(j,paste(0:9)))==1)}
> combien
[1] 3456
And a bonus one:
Find all integers y that can write both as x³ and (10z)³+a with 1≤a≤999.
which does not offer much in terms of solutions since x³-v³=(x-v)(x²+xv+v²)=a shows that x² is less than 2a/3, meaning x is at most 25. Among such numbers only x=11,12 lead to a solution as x³=1331,1728.
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