Archive for stringr:str_count

Le Monde puzzle [#1094]

Posted in Books, Kids, R with tags , , , , , , on April 23, 2019 by xi'an

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){
> 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.