Solution to: https://pbs.twimg.com/media/DXNgwyUWkAIdhtu.jpg

solution.py

#!/usr/bin/env python3

import itertools


A, B, C, D = [1, 2, 3, 4]

iterer = itertools.product([A, B, C, D], repeat=10)

for comb in iterer:
    q1, q2, q3, q4, q5, q6, q7, q8, q9, q10 = comb
    countA = len([i for i in comb if i == A])
    countB = len([i for i in comb if i == B])
    countC = len([i for i in comb if i == C])
    countD = len([i for i in comb if i == D])
    minOpt = min([countA, countB, countC, countD])
    maxOpt = max([countA, countB, countC, countD])


    if not (
        (q2 == A and q5 == C) or
        (q2 == B and q5 == D) or
        (q2 == C and q5 == A) or
        (q2 == D and q5 == B)
    ): continue
    if not (
        (q3 == A and q3 != q6 and q3 != q2 and q3 != q4) or
        (q3 == B and q6 != q3 and q6 != q2 and q6 != q4) or
        (q3 == C and q2 != q3 and q2 != q6 and q2 != q4) or
        (q3 == D and q4 != q3 and q4 != q6 and q4 != q2)
    ): continue
    if not (
        (q4 == A and q1 == q5) or
        (q4 == B and q2 == q7) or
        (q4 == C and q1 == q9) or
        (q4 == D and q6 == q10)
    ): continue
    if not (
        (q5 == A and q5 == q8) or
        (q5 == B and q5 == q4) or
        (q5 == C and q5 == q9) or
        (q5 == D and q5 == q7)
    ): continue
    if not (
        (q6 == A and q8 == q2 and q8 == q4) or
        (q6 == B and q8 == q1 and q8 == q6) or
        (q6 == C and q8 == q3 and q8 == q10) or
        (q6 == D and q8 == q5 and q8 == q9)
    ): continue
    if not(
        (q7 == A and countC == minOpt) or
        (q7 == B and countB == minOpt) or
        (q7 == C and countA == minOpt) or
        (q7 == D and countD == minOpt)
    ): continue
    if not(
        (q8 == A and abs(q1 - q7) > 1) or
        (q8 == B and abs(q1 - q5) > 1) or
        (q8 == C and abs(q1 - q2) > 1) or
        (q8 == D and abs(q1 - q10) > 1)
    ):
        continue
    if not (
        (q9 == A and ((q1 == q6) ^ (q6 == q5))) or
        (q9 == B and ((q1 == q6) ^ (q10 == q5))) or
        (q9 == C and ((q1 == q6) ^ (q2 == q5))) or
        (q9 == D and ((q1 == q6) ^ (q9 == q5)))
    ): continue
    if not (
        (q10 == A and 3 == maxOpt - minOpt) or
        (q10 == B and 2 == maxOpt - minOpt) or
        (q10 == C and 4 == maxOpt - minOpt) or
        (q10 == D and 1 == maxOpt - minOpt)
    ): continue


    print(comb)

print("done")