perplexus.info :: Numbers : 6-digit number

6-digit number (Posted on 2022-09-07)

ABCDEF is a 6-digit number where each of the digits is different.

A, C, and E are odd and in increasing order.
B, D and F are even.
Any two adjacent digits differ by at least 2.
The 2-digit numbers CD and EF are each a multiple of AB.

What is the 6-digit number?

From Mensa Puzzle Calendar 2022 by Fraser Simpson, Workman Publishing, New York. Puzzle for August 30.

Submitted by Charlie

Rating: 5.0000 (1 votes)

Solution: (Hide)

ace=nchoosek('13579',3); bdf=nchoosek('02468',3); bdfp=''; for i=1:length(bdf) bdfp=[bdfp; perms(bdf(i,:))]; end for i=1:length(ace) for j=1:length(bdfp) n=''; for k=1:3 n=[n ace(i,k) bdfp(j,k)]; end good=true; for k=1:5 if abs(n(k)-n(k+1))<2 good=false; end end if good cd=str2num(n(3:4)); ef=str2num(n(5:6)); ab=str2num(n(1:2)); if round(cd/ab)==cd/ab && round(ef/ab)==ef/ab disp(n) end end end end 183690

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-09-07 07:04:51
By Trial and Error (Spoiler)	Steve Herman	2022-09-07 06:53:02

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