All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Y ask about Y ? (Posted on 2017-04-04) Difficulty: 2 of 5
(i)Y is a positive integer.
(ii) Y-1 is divisible by 5;
(iii) Y is divisible by 2,3,4,6,7,8 and 9.

What is the smallest Y?.

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Another approach | Comment 2 of 5 |
The LCM of all integers 2-9 is 2520.  Then Y*(Y-1) = 2520*n, which implies Y = (1 +/- sqrt[1+10080*n])/2

The first n which makes Y an integer is n=20 yielding Y=225 and Y-1=224.  But that has Y as a multiple of 3,5,9 and Y-1 as a multiple of 2,4,7,8 and neither a multiple of 6.  

So I keep going until I find n=101 (the fifth n that yields integer Y) which yields Y=505 and Y-1=504.  This almost works, Y is a multiple of 5 and Y-1 is a multiple of 2,3,4,6,7,8,9 - the exact opposite of what the problem asks.

Keep going until I finally find n=1612 (the eleventh n) which yields Y=2016 and Y-1=2015.  This is what we want, Y is a multiple of 2,3,4,6,7,8,9 and Y-1 is a multiple of 5.

This is obviously slower than Steve's direct approach.

  Posted by Brian Smith on 2017-04-04 12:25:42
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information