[seqfan] Cut N into L & S --now N/L leaves S as remainder

Eric Angelini Eric.Angelini at kntv.be
Thu Dec 10 20:27:10 CET 2009

Hello SeqFans,
after my post on Math-Fun and a couple of mails with people who helped
me, I'm happy to provide you with this puzzle:

(1) choose an integer N
(2) cut N into two substrings X and Y, none of which starts with a zero
(3) see X and Y as integers
(4) call L the largest integer and S the smallest one
(5) check that for any legal cut of N the operation N/B leaves S as remainder

Take for instance N = 9243:

The 1st cut is 924<>3 thus L=924 and S=3. Yes, N/L leaves S: 9243/924 --> 3
The 2nd cut is 92<>43 thus L=92 and S=43. Yes, N/L leaves S: 9243/92 --> 43        
The 3rd cut is 9<>243 thus L=243 and S=9. Yes, N/L leaves S: 9243/243 --> 9        

What is the next integer both having this property and showing four different
digits (as 9243 does)? The previous one was 8216.


No spoiler here -- but 9243 and 8216 are at the end of the page (in French):

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