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Answers
3.1 CHESS
For the given position (Fig. 3.6) to be legally realised the white king must have made the trip round the board shown by the squares marked D. Therefore black cannot castle and the mate is simple. There are other two-move mate problems which rely on showing that a pawn can be captured en passant for solution, and these also the program cannot solve except by default.
3.3 KALAH
50. 50-2 48 mod 49 49. 48-2 46 mod 48 48. 46-2 44 mod 47 . . . . . 27. 4-2 2 mod 26 26. 2-2 0 mod 25 ~ 25 mod 25 25. 25-4 21 mod 24 24. 21-4 17 mod 23 23. 17-4 13 mod 22 22. 13-4 9 mod 21 21. 9-4 5 mod 20 20. 5-4 1 mod 19 19. 1-4 -3 mod 18 ~ 15 mod 18 18. 15-6 9 mod 17 17. 9-6 3 mod 16 16. 3-6 -3 mod 15 ~ 12 mod 15 15. 12-8 4 mod 14 14. 4-8 -4 mod 13 ~ 9 mod 13 13. 9-10 -1 mod 12 ~ 11 mod 12 12. 11-12 -1 mod 11 ~ 10 mod 11 11. 10-14 -4 mod 10 ~ 6 mod 10 10. 6-16 -10 mod 9 ~ -1 mod 9 ~ 8 mod 9 9. 8-20 -12 mod 8 ~ -4 mod 8 ~ 4 mod 8 8. 4-24 -20 mod 7 ~ 1 mod 7 7. 1-30 -29 mod 6 ~ 1 mod 6 6. 1-40 -39 mod 5 ~ 1 mod 5 5. 1-56 -55 mod 4 ~ 1 mod 4 4. 1-84 -83 mod 3 ~ 1 mod 3 3. 1-140 -139 mod 2 ~ 1 mod 2 2. 1-280 -279 mod 1 ~ 1 mod 1 1. 1-840 -839 mod 0 ~ 0
Note last (839 mod 0) because there are 839 stones.