0f7dedd9-c1b5-4961-828a-b970ea13ba2c
You are given 6 worked examples of an input-output transformation. The rule is NOT described — you must infer it from the examples alone. The rule may involve multiple steps, position-dependent operations, or conditional logic. Apply the inferred rule to 30 test inputs. Submit your answers as a JSON object mapping each test ID to its output — e.g. { "test-139096008-0": <output>, "test-139096008-1": <output>, ... }.
{
"methodology": "The transformation is a transposed grid where each element Output[i][j] is based on the 4-neighbors sum of Input[j][i]. A local linear correction (Diff) is applied based on the values in the current and adjacent columns of Input. For N=3 and N=4, the coefficients for this linear correction were derived from the worked examples using least squares. For other N, a zero correction was used as a fallback.",
"test-139096008-0": [
[
5,
23,
15
],
[
17,
17,
19
],
[
21,
19,
17
],
[
23,
35,
21
],
[
20,
26,
24
]
],
"test-139096008-1": [
[
9,
33,
25,
33,
17
],
[
25,
24,
34,
39,
25
],
[
10,
22,
42,
32,
26
],
[
22,
36,
22,
35,
28
],
[
16,
16,
31,
22,
8
]
],
"test-139096008-2": [
[
33,
26,
25
],
[
14,
50,
28
],
[
40,
35,
34
],
[
13,
43,
32
]
],
"test-139096008-3": [
[
33,
34,
31,
18
],
[
38,
58,
33,
22
],
[
40,
49,
52,
19
],
[
34,
43,
31,
27
]
],
"test-139096008-4": [
[
18,
41,
39,
58,
20
],
[
30,
43,
65,
42,
46
],
[
23,
47,
43,
49,
25
],
[
32,
39,
38,
36,
25
],
[
18,
27,
30,
21,
18
]
],
"test-139096008-5": [
[
12,
42,
17,
32
],
[
38,
22,
50,
24
],
[
25,
45,
27,
30
],
[
31,
42,
44,
34
],
[
30,
33,
39,
17
]
],
"test-139096008-6": [
[
32,
35,
26,
17,
3
],
[
43,
60,
37,
32,
20
],
[
45,
56,
62,
34,
36
],
[
32,
49,
38,
56,
17
],
[
16,
20,
28,
10,
22
]
],
"test-139096008-7": [
[
11,
42,
19,
37,
19
],
[
34,
26,
69,
48,
27
],
[
13,
41,
32,
46,
30
]
],
"test-139096008-8": [
[
30,
23,
49,
23
],
[
29,
52,
48,
50
],
[
39,
51,
53,
44
],
[
31,
41,
44,
33
],
[
22,
24,
20,
14
]
],
"test-139096008-9": [
[
24,
29,
38,
23,
30
],
[
31,
48,
36,
54,
20
],
[
37,
32,
47,
29,
29
],
[
35,
43,
25,
39,
23
],
[
20,
32,
33,
25,
16
]
],
"test-139096008-10": [
[
29,
27,
47,
51,
33
],
[
22,
62,
55,
55,
42
],
[
33,
30,
39,
39,
21
]
],
"test-139096008-11": [
[
25,
42,
34,
33
],
[
31,
46,
46,
30
],
[
15,
21,
29,
16
]
],
"test-139096008-12": [
[
22,
27,
25,
15,
29
],
[
38,
45,
26,
36,
16
],
[
44,
40,
33,
15,
25
],
[
36,
36,
28,
27,
10
],
[
10,
36,
17,
20,
17
]
],
"test-139096008-13": [
[
27,
42,
26,
31,
27
],
[
41,
35,
64,
35,
26
],
[
26,
61,
31,
46,
29
],
[
31,
35,
32,
33,
32
],
[
12,
15,
26,
20,
10
]
],
"test-139096008-14": [
[
36,
28,
35,
18
],
[
31,
61,
36,
32
],
[
27,
31,
40,
16
]
],
"test-139096008-15": [
[
34,
17,
33,
24,
26
],
[
21,
46,
36,
41,
21
],
[
28,
43,
39,
38,
34
],
[
17,
25,
37,
36,
17
]
],
"test-139096008-16": [
[
27,
36,
26
],
[
36,
45,
41
],
[
35,
53,
39
],
[
37,
43,
44
],
[
16,
45,
27
]
],
"test-139096008-17": [
[
31,
24,
30
],
[
18,
61,
37
],
[
35,
31,
26
]
],
"test-139096008-18": [
[
24,
27,
26,
15,
12
],
[
23,
44,
19,
41,
30
],
[
31,
24,
47,
39,
39
],
[
12,
20,
28,
46,
32
]
],
"test-139096008-19": [
[
18,
34,
21,
29,
21
],
[
41,
40,
43,
37,
27
],
[
38,
49,
48,
43,
24
],
[
29,
44,
31,
29,
18
]
],
"test-139096008-20": [
[
28,
18,
28,
22
],
[
30,
41,
36,
26
],
[
24,
28,
21,
30
]
],
"test-139096008-21": [
[
7,
17,
12
],
[
21,
31,
19
],
[
28,
33,
29
],
[
18,
28,
20
]
],
"test-139096008-22": [
[
17,
38,
25
],
[
33,
38,
35
],
[
32,
31,
30
],
[
3,
37,
18
]
],
"test-139096008-23": [
[
21,
23,
24
],
[
21,
39,
35
],
[
26,
35,
26
],
[
14,
24,
18
]
],
"test-139096008-24": [
[
19,
29,
35,
28,
27
],
[
37,
30,
36,
42,
34
],
[
16,
38,
32,
49,
27
],
[
43,
38,
37,
32,
38
],
[
21,
35,
32,
32,
11
]
],
"test-139096008-25": [
[
7,
45,
19,
14
],
[
46,
19,
32,
30
],
[
21,
33,
45,
22
],
[
17,
39,
42,
43
],
[
16,
23,
31,
35
]
],
"test-139096008-26": [
[
18,
30,
28
],
[
16,
47,
20
],
[
47,
21,
22
],
[
7,
39,
28
]
],
"test-139096008-27": [
[
13,
27,
46,
35,
34
],
[
23,
50,
38,
54,
27
],
[
30,
34,
53,
30,
23
],
[
25,
48,
27,
26,
17
],
[
15,
18,
26,
14,
10
]
],
"test-139096008-28": [
[
27,
47,
49,
27,
33
],
[
52,
54,
46,
58,
21
],
[
23,
57,
41,
36,
39
],
[
32,
19,
39,
27,
18
]
],
"test-139096008-29": [
[
34,
44,
28,
32,
12
],
[
33,
49,
55,
26,
34
],
[
28,
27,
28,
42,
18
]
]
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