Neighbor-Sum Grids
Statement
Goal
A (2-)neighbor-sum grid is a 5×5 matrix containing each number fromExample: (21 = 4+17, 14 = 4+10, 10 = 4+6, 16 = 6+10, 22 = 6+16, etc for every value >2 of the grid)
21 14 10 16 22
17 4 1 6 19
12 3 5 11 13
15 8 2 7 18
23 24 9 20 25
It can be proven that there are 56816 such grids (or 7102 up to the 8 symmetries of the square).
In this problem, you are given a partially completed grid (in which unknown values are indicated by a
Input
5 lines of 5 space-separated numbers between 0 and 25 , 0 indicating an unknown value.
Output
5 lines of 5 space-separated numbers between 1 and 25 corresponding to the unique complete solution.
Constraints
Example
Input
21 14 10 0 0 0 4 1 6 0 0 3 5 11 13 15 0 0 0 0 23 24 0 20 25
Output
21 14 10 16 22 17 4 1 6 19 12 3 5 11 13 15 8 2 7 18 23 24 9 20 25
Tags
Backtracking
Difficulty
Hard
Test cases
10 missing Test
Input
21 14 10 0 0
0 4 1 6 0
0 3 5 11 13
15 0 0 0 0
23 24 0 20 25
Output
21 14 10 16 22
17 4 1 6 19
12 3 5 11 13
15 8 2 7 18
23 24 9 20 25
Validator 1 Validator
Input
0 0 0 20 21
0 6 5 4 0
23 7 1 3 0
0 9 8 2 0
25 24 0 0 22
Output
19 11 15 20 21
13 6 5 4 17
23 7 1 3 14
16 9 8 2 12
25 24 18 10 22
13 missing Test
Input
19 15 11 0 23
0 0 0 0 13
0 0 1 0 22
0 0 0 0 16
14 12 21 0 25
Output
19 15 11 17 23
18 4 5 6 13
20 3 1 7 22
2 10 8 9 16
14 12 21 24 25
Validator 2 Validator
Input
21 13 0 0 23
10 0 0 0 0
12 2 3 6 15
0 0 4 0 0
0 0 11 0 17
Output
21 13 22 14 23
10 8 5 9 24
12 2 3 6 15
19 7 4 1 16
25 18 11 20 17
16 missing Test
Input
23 22 8 0 18
0 0 0 5 0
0 0 12 0 0
0 10 0 11 9
0 0 0 0 0
Output
23 22 8 13 18
19 1 3 5 25
15 4 12 2 7
14 10 6 11 9
24 16 21 17 20
Validator 3 Validator
Input
0 11 8 0 0
0 0 3 0 0
18 0 23 2 0
0 0 0 0 0
24 0 21 15 0
Output
20 11 8 25 17
19 1 3 5 12
18 4 23 2 7
14 10 6 13 9
24 16 21 15 22
19 missing Test
Input
0 12 0 0 0
0 0 17 0 7
0 4 3 0 18
0 0 0 0 0
0 0 0 0 0
Output
23 12 13 20 25
11 1 17 5 7
10 4 3 2 18
19 9 6 8 16
24 15 21 14 22
Validator 4 Validator
Input
0 0 0 16 0
10 0 0 0 0
0 0 2 0 0
21 0 0 0 24
0 0 0 11 0
Output
25 15 13 16 23
10 6 9 7 12
22 4 2 5 20
21 1 3 8 24
18 17 14 11 19
22 missing Test
Input
0 0 0 0 0
0 0 0 0 0
0 0 17 0 0
0 0 0 5 0
0 0 0 13 0
Output
24 16 21 15 20
14 10 6 11 9
18 4 17 2 7
19 1 3 5 12
23 22 8 13 25
Validator 5 Validator
Input
0 0 0 0 0
9 0 0 0 0
0 0 19 0 0
0 0 0 0 0
0 0 0 11 0
Output
25 15 21 20 24
9 16 6 10 14
7 2 19 4 18
12 5 3 1 22
17 13 8 11 23
22 missing Test
Input
0 0 8 13 0
0 0 0 0 0
0 0 15 0 0
0 0 0 0 0
0 0 0 0 0
Output
23 22 8 13 25
19 1 3 5 12
18 4 15 2 7
14 10 6 11 9
24 16 21 17 20
Validator 6 Validator
Input
0 0 0 0 0
0 0 0 0 0
0 0 7 0 0
19 0 0 0 5
0 0 0 0 0
Output
22 14 20 16 25
24 8 6 10 15
17 2 7 4 11
19 9 3 1 5
21 12 13 18 23
23 missing Test
Input
0 0 0 0 0
0 0 0 0 0
0 0 18 0 0
23 0 0 0 0
0 0 0 0 0
Output
19 12 13 16 17
7 5 3 1 20
9 2 18 4 11
23 8 6 10 15
22 14 24 21 25
Validator 7 Validator
Input
0 0 0 7 0
0 0 0 0 0
0 0 18 0 0
0 0 0 0 0
0 0 0 0 0
Output
22 23 9 7 19
14 8 2 5 12
24 6 18 3 13
21 10 4 1 16
25 15 11 20 17
23 missing Test
Input
21 0 1 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
Output
21 11 1 13 18
10 4 3 5 12
20 6 2 7 19
14 8 15 9 16
22 23 17 24 25
Validator 8 Validator
Input
18 0 1 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
Output
18 13 1 11 21
12 5 3 4 10
19 7 2 6 20
16 9 15 8 14
25 24 17 23 22
Solution language
Solution
Stub generator input