Sun Feb 5 07:48:53 2023 football2_diophantine_test(): Python version: 3.8.10 football2_diophantine() finds the ways to achieve a score of N points in football, given individual options of 2, 3, 4, 6, 7, 8 options. Here, the order does not matter, just the number of times each scoring opportunity was achieved. 0 1 [[0. 0. 0. 0. 0.]] 1 0 2 1 [[1. 0. 0. 0. 0.]] 3 1 [[0. 1. 0. 0. 0.]] 4 1 [[2. 0. 0. 0. 0.]] 5 1 [[1. 1. 0. 0. 0.]] 6 3 [[3. 0. 0. 0. 0.] [0. 2. 0. 0. 0.] [0. 0. 1. 0. 0.]] 7 2 [[2. 1. 0. 0. 0.] [0. 0. 0. 1. 0.]] 8 4 [[4. 0. 0. 0. 0.] [1. 2. 0. 0. 0.] [1. 0. 1. 0. 0.] [0. 0. 0. 0. 1.]] 9 4 [[3. 1. 0. 0. 0.] [1. 0. 0. 1. 0.] [0. 3. 0. 0. 0.] [0. 1. 1. 0. 0.]] 10 5 [[5. 0. 0. 0. 0.] [2. 2. 0. 0. 0.] [2. 0. 1. 0. 0.] [1. 0. 0. 0. 1.] [0. 1. 0. 1. 0.]] 11 5 [[4. 1. 0. 0. 0.] [2. 0. 0. 1. 0.] [1. 3. 0. 0. 0.] [1. 1. 1. 0. 0.] [0. 1. 0. 0. 1.]] 12 8 [[6. 0. 0. 0. 0.] [3. 2. 0. 0. 0.] [3. 0. 1. 0. 0.] [2. 0. 0. 0. 1.] [1. 1. 0. 1. 0.] [0. 4. 0. 0. 0.] [0. 2. 1. 0. 0.] [0. 0. 2. 0. 0.]] 13 7 [[5. 1. 0. 0. 0.] [3. 0. 0. 1. 0.] [2. 3. 0. 0. 0.] [2. 1. 1. 0. 0.] [1. 1. 0. 0. 1.] [0. 2. 0. 1. 0.] [0. 0. 1. 1. 0.]] 14 11 [[7. 0. 0. 0. 0.] [4. 2. 0. 0. 0.] [4. 0. 1. 0. 0.] [3. 0. 0. 0. 1.] [2. 1. 0. 1. 0.] [1. 4. 0. 0. 0.] [1. 2. 1. 0. 0.] [1. 0. 2. 0. 0.] [0. 2. 0. 0. 1.] [0. 0. 1. 0. 1.] [0. 0. 0. 2. 0.]] 15 11 [[6. 1. 0. 0. 0.] [4. 0. 0. 1. 0.] [3. 3. 0. 0. 0.] [3. 1. 1. 0. 0.] [2. 1. 0. 0. 1.] [1. 2. 0. 1. 0.] [1. 0. 1. 1. 0.] [0. 5. 0. 0. 0.] [0. 3. 1. 0. 0.] [0. 1. 2. 0. 0.] [0. 0. 0. 1. 1.]] 16 14 [[8. 0. 0. 0. 0.] [5. 2. 0. 0. 0.] [5. 0. 1. 0. 0.] [4. 0. 0. 0. 1.] [3. 1. 0. 1. 0.] [2. 4. 0. 0. 0.] [2. 2. 1. 0. 0.] [2. 0. 2. 0. 0.] [1. 2. 0. 0. 1.] [1. 0. 1. 0. 1.] [1. 0. 0. 2. 0.] [0. 3. 0. 1. 0.] [0. 1. 1. 1. 0.] [0. 0. 0. 0. 2.]] 17 14 [[7. 1. 0. 0. 0.] [5. 0. 0. 1. 0.] [4. 3. 0. 0. 0.] [4. 1. 1. 0. 0.] [3. 1. 0. 0. 1.] [2. 2. 0. 1. 0.] [2. 0. 1. 1. 0.] [1. 5. 0. 0. 0.] [1. 3. 1. 0. 0.] [1. 1. 2. 0. 0.] [1. 0. 0. 1. 1.] [0. 3. 0. 0. 1.] [0. 1. 1. 0. 1.] [0. 1. 0. 2. 0.]] 18 19 [[9. 0. 0. 0. 0.] [6. 2. 0. 0. 0.] [6. 0. 1. 0. 0.] [5. 0. 0. 0. 1.] [4. 1. 0. 1. 0.] [3. 4. 0. 0. 0.] [3. 2. 1. 0. 0.] [3. 0. 2. 0. 0.] [2. 2. 0. 0. 1.] [2. 0. 1. 0. 1.] [2. 0. 0. 2. 0.] [1. 3. 0. 1. 0.] [1. 1. 1. 1. 0.] [1. 0. 0. 0. 2.] [0. 6. 0. 0. 0.] [0. 4. 1. 0. 0.] [0. 2. 2. 0. 0.] [0. 1. 0. 1. 1.] [0. 0. 3. 0. 0.]] 19 18 [[8. 1. 0. 0. 0.] [6. 0. 0. 1. 0.] [5. 3. 0. 0. 0.] [5. 1. 1. 0. 0.] [4. 1. 0. 0. 1.] [3. 2. 0. 1. 0.] [3. 0. 1. 1. 0.] [2. 5. 0. 0. 0.] [2. 3. 1. 0. 0.] [2. 1. 2. 0. 0.] [2. 0. 0. 1. 1.] [1. 3. 0. 0. 1.] [1. 1. 1. 0. 1.] [1. 1. 0. 2. 0.] [0. 4. 0. 1. 0.] [0. 2. 1. 1. 0.] [0. 1. 0. 0. 2.] [0. 0. 2. 1. 0.]] 20 24 [[10. 0. 0. 0. 0.] [ 7. 2. 0. 0. 0.] [ 7. 0. 1. 0. 0.] [ 6. 0. 0. 0. 1.] [ 5. 1. 0. 1. 0.] [ 4. 4. 0. 0. 0.] [ 4. 2. 1. 0. 0.] [ 4. 0. 2. 0. 0.] [ 3. 2. 0. 0. 1.] [ 3. 0. 1. 0. 1.] [ 3. 0. 0. 2. 0.] [ 2. 3. 0. 1. 0.] [ 2. 1. 1. 1. 0.] [ 2. 0. 0. 0. 2.] [ 1. 6. 0. 0. 0.] [ 1. 4. 1. 0. 0.] [ 1. 2. 2. 0. 0.] [ 1. 1. 0. 1. 1.] [ 1. 0. 3. 0. 0.] [ 0. 4. 0. 0. 1.] [ 0. 2. 1. 0. 1.] [ 0. 2. 0. 2. 0.] [ 0. 0. 2. 0. 1.] [ 0. 0. 1. 2. 0.]] 21 25 [[9. 1. 0. 0. 0.] [7. 0. 0. 1. 0.] [6. 3. 0. 0. 0.] [6. 1. 1. 0. 0.] [5. 1. 0. 0. 1.] [4. 2. 0. 1. 0.] [4. 0. 1. 1. 0.] [3. 5. 0. 0. 0.] [3. 3. 1. 0. 0.] [3. 1. 2. 0. 0.] [3. 0. 0. 1. 1.] [2. 3. 0. 0. 1.] [2. 1. 1. 0. 1.] [2. 1. 0. 2. 0.] [1. 4. 0. 1. 0.] [1. 2. 1. 1. 0.] [1. 1. 0. 0. 2.] [1. 0. 2. 1. 0.] [0. 7. 0. 0. 0.] [0. 5. 1. 0. 0.] [0. 3. 2. 0. 0.] [0. 2. 0. 1. 1.] [0. 1. 3. 0. 0.] [0. 0. 1. 1. 1.] [0. 0. 0. 3. 0.]] 22 30 [[11. 0. 0. 0. 0.] [ 8. 2. 0. 0. 0.] [ 8. 0. 1. 0. 0.] [ 7. 0. 0. 0. 1.] [ 6. 1. 0. 1. 0.] [ 5. 4. 0. 0. 0.] [ 5. 2. 1. 0. 0.] [ 5. 0. 2. 0. 0.] [ 4. 2. 0. 0. 1.] [ 4. 0. 1. 0. 1.] [ 4. 0. 0. 2. 0.] [ 3. 3. 0. 1. 0.] [ 3. 1. 1. 1. 0.] [ 3. 0. 0. 0. 2.] [ 2. 6. 0. 0. 0.] [ 2. 4. 1. 0. 0.] [ 2. 2. 2. 0. 0.] [ 2. 1. 0. 1. 1.] [ 2. 0. 3. 0. 0.] [ 1. 4. 0. 0. 1.] [ 1. 2. 1. 0. 1.] [ 1. 2. 0. 2. 0.] [ 1. 0. 2. 0. 1.] [ 1. 0. 1. 2. 0.] [ 0. 5. 0. 1. 0.] [ 0. 3. 1. 1. 0.] [ 0. 2. 0. 0. 2.] [ 0. 1. 2. 1. 0.] [ 0. 0. 1. 0. 2.] [ 0. 0. 0. 2. 1.]] 23 31 [[10. 1. 0. 0. 0.] [ 8. 0. 0. 1. 0.] [ 7. 3. 0. 0. 0.] [ 7. 1. 1. 0. 0.] [ 6. 1. 0. 0. 1.] [ 5. 2. 0. 1. 0.] [ 5. 0. 1. 1. 0.] [ 4. 5. 0. 0. 0.] [ 4. 3. 1. 0. 0.] [ 4. 1. 2. 0. 0.] [ 4. 0. 0. 1. 1.] [ 3. 3. 0. 0. 1.] [ 3. 1. 1. 0. 1.] [ 3. 1. 0. 2. 0.] [ 2. 4. 0. 1. 0.] [ 2. 2. 1. 1. 0.] [ 2. 1. 0. 0. 2.] [ 2. 0. 2. 1. 0.] [ 1. 7. 0. 0. 0.] [ 1. 5. 1. 0. 0.] [ 1. 3. 2. 0. 0.] [ 1. 2. 0. 1. 1.] [ 1. 1. 3. 0. 0.] [ 1. 0. 1. 1. 1.] [ 1. 0. 0. 3. 0.] [ 0. 5. 0. 0. 1.] [ 0. 3. 1. 0. 1.] [ 0. 3. 0. 2. 0.] [ 0. 1. 2. 0. 1.] [ 0. 1. 1. 2. 0.] [ 0. 0. 0. 1. 2.]] 24 39 [[12. 0. 0. 0. 0.] [ 9. 2. 0. 0. 0.] [ 9. 0. 1. 0. 0.] [ 8. 0. 0. 0. 1.] [ 7. 1. 0. 1. 0.] [ 6. 4. 0. 0. 0.] [ 6. 2. 1. 0. 0.] [ 6. 0. 2. 0. 0.] [ 5. 2. 0. 0. 1.] [ 5. 0. 1. 0. 1.] [ 5. 0. 0. 2. 0.] [ 4. 3. 0. 1. 0.] [ 4. 1. 1. 1. 0.] [ 4. 0. 0. 0. 2.] [ 3. 6. 0. 0. 0.] [ 3. 4. 1. 0. 0.] [ 3. 2. 2. 0. 0.] [ 3. 1. 0. 1. 1.] [ 3. 0. 3. 0. 0.] [ 2. 4. 0. 0. 1.] [ 2. 2. 1. 0. 1.] [ 2. 2. 0. 2. 0.] [ 2. 0. 2. 0. 1.] [ 2. 0. 1. 2. 0.] [ 1. 5. 0. 1. 0.] [ 1. 3. 1. 1. 0.] [ 1. 2. 0. 0. 2.] [ 1. 1. 2. 1. 0.] [ 1. 0. 1. 0. 2.] [ 1. 0. 0. 2. 1.] [ 0. 8. 0. 0. 0.] [ 0. 6. 1. 0. 0.] [ 0. 4. 2. 0. 0.] [ 0. 3. 0. 1. 1.] [ 0. 2. 3. 0. 0.] [ 0. 1. 1. 1. 1.] [ 0. 1. 0. 3. 0.] [ 0. 0. 4. 0. 0.] [ 0. 0. 0. 0. 3.]] 25 38 [[11. 1. 0. 0. 0.] [ 9. 0. 0. 1. 0.] [ 8. 3. 0. 0. 0.] [ 8. 1. 1. 0. 0.] [ 7. 1. 0. 0. 1.] [ 6. 2. 0. 1. 0.] [ 6. 0. 1. 1. 0.] [ 5. 5. 0. 0. 0.] [ 5. 3. 1. 0. 0.] [ 5. 1. 2. 0. 0.] [ 5. 0. 0. 1. 1.] [ 4. 3. 0. 0. 1.] [ 4. 1. 1. 0. 1.] [ 4. 1. 0. 2. 0.] [ 3. 4. 0. 1. 0.] [ 3. 2. 1. 1. 0.] [ 3. 1. 0. 0. 2.] [ 3. 0. 2. 1. 0.] [ 2. 7. 0. 0. 0.] [ 2. 5. 1. 0. 0.] [ 2. 3. 2. 0. 0.] [ 2. 2. 0. 1. 1.] [ 2. 1. 3. 0. 0.] [ 2. 0. 1. 1. 1.] [ 2. 0. 0. 3. 0.] [ 1. 5. 0. 0. 1.] [ 1. 3. 1. 0. 1.] [ 1. 3. 0. 2. 0.] [ 1. 1. 2. 0. 1.] [ 1. 1. 1. 2. 0.] [ 1. 0. 0. 1. 2.] [ 0. 6. 0. 1. 0.] [ 0. 4. 1. 1. 0.] [ 0. 3. 0. 0. 2.] [ 0. 2. 2. 1. 0.] [ 0. 1. 1. 0. 2.] [ 0. 1. 0. 2. 1.] [ 0. 0. 3. 1. 0.]] 26 47 [[13. 0. 0. 0. 0.] [10. 2. 0. 0. 0.] [10. 0. 1. 0. 0.] [ 9. 0. 0. 0. 1.] [ 8. 1. 0. 1. 0.] [ 7. 4. 0. 0. 0.] [ 7. 2. 1. 0. 0.] [ 7. 0. 2. 0. 0.] [ 6. 2. 0. 0. 1.] [ 6. 0. 1. 0. 1.] [ 6. 0. 0. 2. 0.] [ 5. 3. 0. 1. 0.] [ 5. 1. 1. 1. 0.] [ 5. 0. 0. 0. 2.] [ 4. 6. 0. 0. 0.] [ 4. 4. 1. 0. 0.] [ 4. 2. 2. 0. 0.] [ 4. 1. 0. 1. 1.] [ 4. 0. 3. 0. 0.] [ 3. 4. 0. 0. 1.] [ 3. 2. 1. 0. 1.] [ 3. 2. 0. 2. 0.] [ 3. 0. 2. 0. 1.] [ 3. 0. 1. 2. 0.] [ 2. 5. 0. 1. 0.] [ 2. 3. 1. 1. 0.] [ 2. 2. 0. 0. 2.] [ 2. 1. 2. 1. 0.] [ 2. 0. 1. 0. 2.] [ 2. 0. 0. 2. 1.] [ 1. 8. 0. 0. 0.] [ 1. 6. 1. 0. 0.] [ 1. 4. 2. 0. 0.] [ 1. 3. 0. 1. 1.] [ 1. 2. 3. 0. 0.] [ 1. 1. 1. 1. 1.] [ 1. 1. 0. 3. 0.] [ 1. 0. 4. 0. 0.] [ 1. 0. 0. 0. 3.] [ 0. 6. 0. 0. 1.] [ 0. 4. 1. 0. 1.] [ 0. 4. 0. 2. 0.] [ 0. 2. 2. 0. 1.] [ 0. 2. 1. 2. 0.] [ 0. 1. 0. 1. 2.] [ 0. 0. 3. 0. 1.] [ 0. 0. 2. 2. 0.]] 27 49 [[12. 1. 0. 0. 0.] [10. 0. 0. 1. 0.] [ 9. 3. 0. 0. 0.] [ 9. 1. 1. 0. 0.] [ 8. 1. 0. 0. 1.] [ 7. 2. 0. 1. 0.] [ 7. 0. 1. 1. 0.] [ 6. 5. 0. 0. 0.] [ 6. 3. 1. 0. 0.] [ 6. 1. 2. 0. 0.] [ 6. 0. 0. 1. 1.] [ 5. 3. 0. 0. 1.] [ 5. 1. 1. 0. 1.] [ 5. 1. 0. 2. 0.] [ 4. 4. 0. 1. 0.] [ 4. 2. 1. 1. 0.] [ 4. 1. 0. 0. 2.] [ 4. 0. 2. 1. 0.] [ 3. 7. 0. 0. 0.] [ 3. 5. 1. 0. 0.] [ 3. 3. 2. 0. 0.] [ 3. 2. 0. 1. 1.] [ 3. 1. 3. 0. 0.] [ 3. 0. 1. 1. 1.] [ 3. 0. 0. 3. 0.] [ 2. 5. 0. 0. 1.] [ 2. 3. 1. 0. 1.] [ 2. 3. 0. 2. 0.] [ 2. 1. 2. 0. 1.] [ 2. 1. 1. 2. 0.] [ 2. 0. 0. 1. 2.] [ 1. 6. 0. 1. 0.] [ 1. 4. 1. 1. 0.] [ 1. 3. 0. 0. 2.] [ 1. 2. 2. 1. 0.] [ 1. 1. 1. 0. 2.] [ 1. 1. 0. 2. 1.] [ 1. 0. 3. 1. 0.] [ 0. 9. 0. 0. 0.] [ 0. 7. 1. 0. 0.] [ 0. 5. 2. 0. 0.] [ 0. 4. 0. 1. 1.] [ 0. 3. 3. 0. 0.] [ 0. 2. 1. 1. 1.] [ 0. 2. 0. 3. 0.] [ 0. 1. 4. 0. 0.] [ 0. 1. 0. 0. 3.] [ 0. 0. 2. 1. 1.] [ 0. 0. 1. 3. 0.]] 28 57 [[14. 0. 0. 0. 0.] [11. 2. 0. 0. 0.] [11. 0. 1. 0. 0.] [10. 0. 0. 0. 1.] [ 9. 1. 0. 1. 0.] [ 8. 4. 0. 0. 0.] [ 8. 2. 1. 0. 0.] [ 8. 0. 2. 0. 0.] [ 7. 2. 0. 0. 1.] [ 7. 0. 1. 0. 1.] [ 7. 0. 0. 2. 0.] [ 6. 3. 0. 1. 0.] [ 6. 1. 1. 1. 0.] [ 6. 0. 0. 0. 2.] [ 5. 6. 0. 0. 0.] [ 5. 4. 1. 0. 0.] [ 5. 2. 2. 0. 0.] [ 5. 1. 0. 1. 1.] [ 5. 0. 3. 0. 0.] [ 4. 4. 0. 0. 1.] [ 4. 2. 1. 0. 1.] [ 4. 2. 0. 2. 0.] [ 4. 0. 2. 0. 1.] [ 4. 0. 1. 2. 0.] [ 3. 5. 0. 1. 0.] [ 3. 3. 1. 1. 0.] [ 3. 2. 0. 0. 2.] [ 3. 1. 2. 1. 0.] [ 3. 0. 1. 0. 2.] [ 3. 0. 0. 2. 1.] [ 2. 8. 0. 0. 0.] [ 2. 6. 1. 0. 0.] [ 2. 4. 2. 0. 0.] [ 2. 3. 0. 1. 1.] [ 2. 2. 3. 0. 0.] [ 2. 1. 1. 1. 1.] [ 2. 1. 0. 3. 0.] [ 2. 0. 4. 0. 0.] [ 2. 0. 0. 0. 3.] [ 1. 6. 0. 0. 1.] [ 1. 4. 1. 0. 1.] [ 1. 4. 0. 2. 0.] [ 1. 2. 2. 0. 1.] [ 1. 2. 1. 2. 0.] [ 1. 1. 0. 1. 2.] [ 1. 0. 3. 0. 1.] [ 1. 0. 2. 2. 0.] [ 0. 7. 0. 1. 0.] [ 0. 5. 1. 1. 0.] [ 0. 4. 0. 0. 2.] [ 0. 3. 2. 1. 0.] [ 0. 2. 1. 0. 2.] [ 0. 2. 0. 2. 1.] [ 0. 1. 3. 1. 0.] [ 0. 0. 2. 0. 2.] [ 0. 0. 1. 2. 1.] [ 0. 0. 0. 4. 0.]] 29 59 [[13. 1. 0. 0. 0.] [11. 0. 0. 1. 0.] [10. 3. 0. 0. 0.] [10. 1. 1. 0. 0.] [ 9. 1. 0. 0. 1.] [ 8. 2. 0. 1. 0.] [ 8. 0. 1. 1. 0.] [ 7. 5. 0. 0. 0.] [ 7. 3. 1. 0. 0.] [ 7. 1. 2. 0. 0.] [ 7. 0. 0. 1. 1.] [ 6. 3. 0. 0. 1.] [ 6. 1. 1. 0. 1.] [ 6. 1. 0. 2. 0.] [ 5. 4. 0. 1. 0.] [ 5. 2. 1. 1. 0.] [ 5. 1. 0. 0. 2.] [ 5. 0. 2. 1. 0.] [ 4. 7. 0. 0. 0.] [ 4. 5. 1. 0. 0.] [ 4. 3. 2. 0. 0.] [ 4. 2. 0. 1. 1.] [ 4. 1. 3. 0. 0.] [ 4. 0. 1. 1. 1.] [ 4. 0. 0. 3. 0.] [ 3. 5. 0. 0. 1.] [ 3. 3. 1. 0. 1.] [ 3. 3. 0. 2. 0.] [ 3. 1. 2. 0. 1.] [ 3. 1. 1. 2. 0.] [ 3. 0. 0. 1. 2.] [ 2. 6. 0. 1. 0.] [ 2. 4. 1. 1. 0.] [ 2. 3. 0. 0. 2.] [ 2. 2. 2. 1. 0.] [ 2. 1. 1. 0. 2.] [ 2. 1. 0. 2. 1.] [ 2. 0. 3. 1. 0.] [ 1. 9. 0. 0. 0.] [ 1. 7. 1. 0. 0.] [ 1. 5. 2. 0. 0.] [ 1. 4. 0. 1. 1.] [ 1. 3. 3. 0. 0.] [ 1. 2. 1. 1. 1.] [ 1. 2. 0. 3. 0.] [ 1. 1. 4. 0. 0.] [ 1. 1. 0. 0. 3.] [ 1. 0. 2. 1. 1.] [ 1. 0. 1. 3. 0.] [ 0. 7. 0. 0. 1.] [ 0. 5. 1. 0. 1.] [ 0. 5. 0. 2. 0.] [ 0. 3. 2. 0. 1.] [ 0. 3. 1. 2. 0.] [ 0. 2. 0. 1. 2.] [ 0. 1. 3. 0. 1.] [ 0. 1. 2. 2. 0.] [ 0. 0. 1. 1. 2.] [ 0. 0. 0. 3. 1.]] football2_diophantine_test(): Normal end of execution. Sun Feb 5 07:48:53 2023