Project Euler Problem 208

This project is based on Project Euler Problem 208, copied with very slight modifications from cemulate's project of the same name.

Try it out!

You can try it out online here. To modify the step size, change the n=5 parameter in the URL. (When omitted, it defaults to n=5.) To modify the intial step sequence, change the w=2,1,3,1,4,1 parameter in the URL. To omit the initial step sequence, change it to w=, w=0 or omit it entirely.

Run locally

Run locally by running python -m SimpleHTTPServer in the project-euler-208 folder.

Related StackExchange questions

• Math Stack Exchange, Area enclosed by robot walk.
• Math Stack Exchange, Non-self-intersecting “Robot Walks”.
• Math Stack Exchange, Points in R^2 that can be reached via steps which are 1/5 of a unit circle.
• Code Golf Stack Exchange, Circular robot instructions.

Table of known values.

n | [i,j]     | intersections
--+-----------+--------------
3 | [1,2]     | 0
--+-----------+--------------
4 | [1,2]     | 0
4 | [2,3]     | 0
4 | [1,3]     | 0
--+-----------+--------------
5 | [1,2]     | 0
5 | [2,3]     | 0
5 | [3,4]     | 0
5 | [1,3]     | 5
5 | [2,4]     | 5
5 | [1,4]     | 10
--+-----------+--------------
6 | [1,2]     | 0
6 | [2,3]     | 0
6 | [3,4]     | 0
6 | [4,5]     | 6
6 | [1,3]     | 0
6 | [2,4]     | 0
6 | [3,5]     | 3
6 | [1,4]     | 0
6 | [2,5]     | 1
6 | [1,5]     | 3
--+-----------+--------------
7 | [1,2]     | 0
7 | [2,3]     | 0
7 | [3,4]     | 0
7 | [4,5]     | 0
7 | [5,6]     | 14
7 | [1,3]     | 7
7 | [2,4]     | 7
7 | [3,5]     | 7
7 | [4,6]     | 21
7 | [1,4]     | 14
7 | [2,5]     | 14
7 | [3,6]     | 42
7 | [1,5]     | 21
7 | [2,6]     | 35
7 | [1,6]     | 28
--+-----------+--------------
8 | [1,2]     | 0
8 | [2,3]     | 0
8 | [3,4]     | 0
8 | [4,5]     | 0
8 | [5,6]     | 0
8 | [6,7]     | 16
8 | [1,3]     | 0
8 | [2,4]     | 0
8 | [3,5]     | 0
8 | [4,6]     | 0
8 | [5,7]     | 8
8 | [1,4]     | 16
8 | [2,5]     | 16
8 | [3,6]     | 16
8 | [4,7]     | 56
8 | [1,5]     | 0
8 | [2,6]     | 0
8 | [3,7]     | 2
8 | [1,6]     | 32
8 | [2,7]     | 40
8 | [1,7]     | 8
9 | [1,2]     | 0
9 | [2,3]     | 0
9 | [3,4]     | 0
9 | [4,5]     | 0
9 | [5,6]     | 0
9 | [6,7]     | 0
9 | [7,8]     | 18
9 | [1,3]     | 9
9 | [2,4]     | 9
9 | [3,5]     | 9
9 | [4,6]     | 9
9 | [5,7]     | 9
9 | [6,8]     | 63
9 | [1,4]     | 0
9 | [2,5]     | 0
9 | [3,6]     | 0
9 | [4,7]     | 0
9 | [5,8]     | 6
9 | [1,5]     | 27
9 | [2,6]     | 27
9 | [3,7]     | 27
9 | [4,8]     | 63
9 | [1,6]     | 36
9 | [2,7]     | 36
9 | [3,8]     | 54
9 | [1,7]     | 3
9 | [2,8]     | 3
9 | [1,8]     | 54
--+-----------+--------------
10 | [1,2]    | 0
10 | [2,3]    | 0
10 | [3,4]    | 0
10 | [4,5]    | 0
10 | [5,6]    | 0
10 | [6,7]    | 0
10 | [7,8]    | 0
10 | [8,9]    | 20
10 | [1,3]    | 0
10 | [2,4]    | 0
10 | [3,5]    | 0
10 | [4,6]    | 0
10 | [5,7]    | 0
10 | [6,8]    | 0
10 | [7,9]    | 15
10 | [1,4]    | 20
10 | [2,5]    | 20
10 | [3,6]    | 20
10 | [4,7]    | 20
10 | [5,8]    | 40
10 | [6,9]    | 90
10 | [1,5]    | 5
10 | [2,6]    | 5
10 | [3,7]    | 5
10 | [4,8]    | 5
10 | [5,9]    | 15
10 | [1,6]    | 0
10 | [2,7]    | 0
10 | [3,8]    | 0
10 | [4,9]    | 2
10 | [1,7]    | 10
10 | [2,8]    | 10
10 | [3,9]    | 15
10 | [1,8]    | 60
10 | [2,9]    | 70
10 | [1,9]    | 15
--+-----------+--------------
11 | [1, 2]   | 0
11 | [2, 3]   | 0
11 | [3, 4]   | 0
11 | [4, 5]   | 0
11 | [5, 6]   | 0
11 | [6, 7]   | 0
11 | [7, 8]   | 0
11 | [8, 9]   | 0
11 | [9, 10]  | 22
11 | [1, 3]   | 11
11 | [2, 4]   | 11
11 | [3, 5]   | 11
11 | [4, 6]   | 11
11 | [5, 7]   | 11
11 | [6, 8]   | 11
11 | [7, 9]   | 33
11 | [8, 10]  | 99
11 | [1, 4]   | 22
11 | [2, 5]   | 22
11 | [3, 6]   | 22
11 | [4, 7]   | 22
11 | [5, 8]   | 22
11 | [6, 9]   | 44
11 | [7, 10]  | 110
11 | [1, 5]   | 33
11 | [2, 6]   | 33
11 | [3, 7]   | 33
11 | [4, 8]   | 33
11 | [5, 9]   | 55
11 | [6, 10]  | 99
11 | [1, 6]   | 44
11 | [2, 7]   | 44
11 | [3, 8]   | 44
11 | [4, 9]   | 88
11 | [5, 10]  | 88
11 | [1, 7]   | 55
11 | [2, 8]   | 55
11 | [3, 9]   | 77
11 | [4, 10]  | 99
11 | [1, 8]   | 66
11 | [2, 9]   | 66
11 | [3, 10]  | 88
11 | [1, 9]   | 77
11 | [2, 10]  | 77
11 | [1, 10]  | 88
--+-----------+--------------
12 | [1,  2]  | 0
12 | [2,  3]  | 0
12 | [3,  4]  | 0
12 | [4,  5]  | 0
12 | [5,  6]  | 0
12 | [6,  7]  | 0
12 | [7,  8]  | 0
12 | [8,  9]  | 0
12 | [9,  10] | 12
12 | [10, 11] | 48
12 | [1,  3]  | 0
12 | [2,  4]  | 0
12 | [3,  5]  | 0
12 | [4,  6]  | 0
12 | [5,  7]  | 0
12 | [6,  8]  | 0
12 | [7,  9]  | 0
12 | [8,  10] | 6
12 | [9,  11] | 24
12 | [1,  4]  | 0
12 | [2,  5]  | 0
12 | [3,  6]  | 0
12 | [4,  7]  | 0
12 | [5,  8]  | 0
12 | [6,  9]  | 0
12 | [7,  10] | 4
12 | [8,  11] | 12
12 | [1,  5]  | 0
12 | [2,  6]  | 0
12 | [3,  7]  | 0
12 | [4,  8]  | 0
12 | [5,  9]  | 0
12 | [6,  10] | 3
12 | [7,  11] | 6
12 | [1,  6]  | 48
12 | [2,  7]  | 48
12 | [3,  8]  | 48
12 | [4,  9]  | 48
12 | [5,  10] | 96
12 | [6,  11] | 108
12 | [1,  7]  | 0
12 | [2,  8]  | 0
12 | [3,  9]  | 0
12 | [4,  10] | 1
12 | [5,  11] | 2
12 | [1,  8]  | 72
12 | [2,  9]  | 72
12 | [3,  10] | 84
12 | [4,  11] | 108
12 | [1,  9]  | 3
12 | [2,  10] | 3
12 | [3,  11] | 3
12 | [1,  10] | 8
12 | [2,  11] | 8
12 | [1,  11] | 24