Le Monde puzzle [#1129]

A number challenge as Le weekly Monde current mathematical puzzle:

When the three consecutive numbers 110, 111 and 112, they all are multiples of the sum of their digits. Are there 4 consecutive numbers with three digits like this? A contrario, does there exist 17 consecutive numbers with three digits such that they cannot be divided by the sum of their digits? 18?

The run of a brute force R search return 510,511,512,513 as the solution to the first question

library(gtools)
bez=!(100:999)%%apply(baseOf(100:999),1,sum)
> (100:897)[bez[-(1:3)]*bez[-c(1:2,900)]*bez[-c(1,899:900)]*bez[-(898:900)]==1]
[1] 510

And to the second one:

> max(diff((1:899)[!!diff(bez)]))
[1] 17

 

2 Responses to “Le Monde puzzle [#1129]”

  1. […] article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here) […]

  2. […] by data_admin [This article was first published on R – Xi’an’s Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.