Number spiral diagonals

2014-09-18

Problem 028: Number spiral diagonals

Description:

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

Solution:

0"d"55+*1+::1-01p*>:01g-:01g-:01g-:01g-:1-#v_>\# :#+_+.@
X ^p10-2g10 <

Start

Pause

Reset

Download

Output:

Stack: (0)

Explanation:

Let's look ate the diagonal numbers of our 5x5 grid:

n	info
25	starting number
21	= 25 - 4
17	= 21 - 4
13	= 17 - 4
9	= 13 - 4
7	= 9 - 2
5	= 7 - 2
3	= 5 - 2
1	= 3 - 2

You can probably see the pattern here. The rest of the algorithm is simply loop from 1001^2 to 1, subtracting the right amount each round and in the end summing up all numbers.

I have this little code to calculate the sum of stack values until a zero is encountered:

>\# :#+_+

Perhaps it's useful for someone else.

Interpreter steps:	28 514
Execution time (BefunExec):	15ms (1.90 MHz)
Program size:	54 x 2 (fully conform befunge-93)
Solution:	669171001
Solved at:	2014-09-18