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The letters in parenthesis are what clues were used to solve the cell.

  1. B: It’s possible that none of the nine numbers appear in B, so therefore Cell B is an X. (A)
  2. C: It’s possible that none of the nine numbers appear in C, so therefore Cell C is an X. (A)
  3. D: We know that 1 is in the first column, and that it cannot be in the fifth row, therefore Cell D is a 1. (B,C)
  4. E: The only number in the fifth row is in the third column, so Cell E is an X. (C)
  5. F: It’s possible that none of the nine numbers appear in F, so therefore Cell F is an X. (A)
  6. G: We know that the second column has more than one number because E’s clue says “numbers.” We know that one of the numbers has to be a 2. We also know that the second number must be even. The only even number it could be is 6 or 8. 8+2=10 and 10 isn’t one of the numbers being guessed. So the two numbers in the second column are 2 and 6. No number can be in the fourth or fifth row of this column, so that means G has to be a number. G is in the second row and we know that 2 cannot be in the second row. So Cell G is a 6. (B,C,D,E,F)
  7. H: The cells in the fourth and fifth row of this column cannot be numbers, and 2 must be in the second column, so Cell H is a 2. (B,C,F)
  8. I: Cell I cannot be a number so Cell I is an X. (F)
  9. J: Cell J cannot be a number so Cell J is an X. (E)
  10. K: We know that no row’s sum is greater than 10 and that 8 and 1 are in the same row. This means that the number 9 must be the only number in its row. We also know that the fifth row only has one number and that that number is in the third column. If that lone number in the fifth column isn’t a 9, then that would mean two rows would have only one number, and that would mean a row would have to have three numbers. No row has more than two numbers, therefore 9 must be in the fifth row and third column. We also know that the third column has exactly two numbers and that one of them is 3. That means the two numbers in the third column are 3 and 9. The 3 cannot go in the second or third row, because then it would be adjacent to another number. The 3 cannot go in the fourth row because then the fourth row’s sum would be greater than 10. So the only place for the 3 to go is in K. Cell K is a 3. (B,C,F,G,H,I)
  11. L: Cell L cannot be a number so Cell L is an X. (F)
  12. M: Cell M cannot be a number so Cell M is an X. (F)
  13. N: We already know that the 9 and 3 are the two numbers in the column, so Cell N is an X. (X)
  14. O: We deducted that 9 must be in this cell earlier, therefore Cell O is a 9.
  15. P: Cell P cannot be a number so Cell P is an X. (F)
  16. Q: We know the second row is the only row whose sum isn’t under ten. We also know that no row’s sum is greater than 10. This means that the second row’s sum is 10. We already have 6 in the second column so the only number that could make the sum 10 is 4. 4 cannot be in the fifth column, so Cell Q must be 4. (B,G,J)
  17. R: Since there is already and even number (4) in the fourth column that means no odd numbers can be in the fourth column. There are only three numbers left: 5, 7, and 8. The fourth row has two numbers, but cannot have a 5 or 7 so the other number must be 8. We know 8 is in the fourth row, so Cell R is an X. (D,H,I)
  18. S: We already deducted that Cell S is an 8 above.
  19. T: There are plenty of reasons why Cell T is an X. One is C’s clue.
  20. U: Cell U has to be a 5, because the 5 cannot go in any other cell. It cannot be in the second or fourth row because of F’s clue. It cannot be in the fifth row because of C’s clue. 5 cannot be in the third row because if a 5 were to go there, then 7 would have to go in the first row. And if 7 were in the first row, then the first row would add up to 10 and that goes against G’s clue. (F,C,G)
  21. V: Cell V cannot be a number so Cell V is an X. (F)
  22. W: There is only one number left (7), and this is the only cell left that can be a number.
  23. X: All the numbers have been discovered so it’s an X.
  24. Y: All the numbers have been discovered so it’s an X.
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