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

Home > Just Math
Going North-East (Posted on 2014-12-05) Difficulty: 3 of 5
On a 10x10 "chessboard" a token is placed on the leftmost square of the bottom line a.k.a. a1.
You can move said token either one step to the right or one step up within the same column or one step diagonally (combining right and up).
To make it clear from c4 you may advance in one step to c5, c6 or d6.

How many distinct routes exist to reach the top line's rightmost square (i.e. j10?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Another way to avoid tedium. | Comment 2 of 4 |
I recognized this as a similar to another problem:

If you only allow right or up steps you generate Pascal's Triangle as the way to count the number of ways of getting to any given square.

Adding the extra move caused me to generate the triangle in a new way:  m(n,r) = m(n-1,r-1) + m(n-1,r) + m(n-2, r-1)
Where m(n,r) is analogous to C(n,r).

The central numbers form the sequence
1, 3, 13, 63, 321

Which, of course is in the OEIS:
https://oeis.org/A001850

The first comment there:
<table cellpadding="2" cellspacing="0"><tbody><tr><td width="20">
</td><td align="left" valign="top" width="100"> COMMENTS </td><td width="600">

Number of paths from (0,0) to (n,n) in an n X n grid using only steps North, Northeast and East (i.e., steps (1,0), (1,1), and (0,1)).

</td></tr></tbody></table>
And the solution is just the 10th term: 1462563

Edited on December 7, 2014, 8:30 pm
  Posted by Jer on 2014-12-06 21:41:37

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information