1. Cell 1 tells us that D is in either Cell 2 or Cell 6. We already know B must be in Cell 2 or Cell 6 because the snake cannot move diagonally and B must come after A. This means B and D are in Cells 2 and 6 (not necessarily that order). This means that C has to be in Cell 7.
2. Since we know that D is in either Cell 2 or 6, which means E must be in Cell 3 or Cell 11. Cell 7 tells us Cell 3 is a consonant, so that means E must be in Cell 11. This also means B must be in Cell 2 and D must be in Cell 6.
3. Cell 11 tells us that I is in Cell 23. The only possible way to get from E to I is for F to be in Cell 16, G to be in Cell 21, and for H to be in Cell 22. There are no other places these letters could go without breaking the rules.
4. Cell 21 tells us that the snake travels three consecutive spaces in the third row going left to right. These spaces have to be Cells 12, 13, and 14. It’s impossible for Cells 13, 14, and 15 to be the three spaces without breaking the rules. Cell 23 tells us that the path doesn’t end in the fifth column. The only possible solution is for J to be in Cell 18, K in Cell 17, L in Cell 12, M in Cell 13, and N in Cell 14. Any other route would break one of the clues or rules.
5. After N, the path can only go one of two ways: up to Cell 9 or down to Cell 19. Either way the path goes, Cell 10 will always be T. There is no path from that point in which Cell 10 isn’t T.
6. Cell T’s clue tells us that is has more consonants than any other row. This means that row doesn’t have any vowels, which means that O cannot go in Cell 9. That means that O must go in Cell 19. From here the only solution is for P to be in Cell 24, Q in Cell 25, R in Cell 20, and S in Cell 15.
7. From here the U can only go in either Cell 9 or Cell 5. If the U was in Cell 9 then the path would end in the fifth, column, so the U must be in Cell 5. This means that the V must be in cell 4.
8. At this point, there are only two possibilities left. In both, Cell 8 is always X. Cell 8 then tells us where the path ends, so Y goes in Cell 9 and W goes in Cell 3.