Le Monde puzzle [#909]

By xi’an

(This article was first published on Xi’an’s Og » R, and kindly contributed to R-bloggers)

Another of those “drop-a-digit” Le Monde mathematical puzzle:

Find all integers n with 3 or 4 digits an single interior zero digit, such that removing that zero digit produces a divider of x.

As in puzzle #904, I made use of the digin R function:


and simply checked all integers up to 10⁶:

for (i in 101:10^6){
 if ((min(dive[1],rev(dive)[1])>0)&
 if (i==((i%/%dive)*dive)){

which leads to the output

> plura
1] 105 108 405 2025 6075 10125 30375 50625 70875
> plura/divid
[1] 7 6 9 9 9 9 9 9 9

leading to the conclusion there is no solution beyond 70875. (Allowing for more than a single zero within the inner digits sees many more solutions.)

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