## Le Monde puzzle [#1094]

**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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