Logic Masters Deutschland e.V.

John and Michael are playing together. However, Michael keeps complaining that he is bored. They’ve played everything he could think of already and he doesn’t always like the games his brother comes up with, as he can’t understand them all. Running out of ideas, John decides to teach his younger brother tic tac toe.
Having explained the rules to Michael they decide to have a match. John picks Xs and starts. Michael shows that he did indeed understand the rules and quickly responds to John’s threats. However, in the end, John outsmarts Michael, and with the last possible move, he wins.
Even though he lost, Michael wants to play again. John agrees, but only if he can have a break to do something he likes. Michael agrees dishearteningly, thinking that, for the next 15 to 30 minutes, he will probably have to watch his sibling solve some boring old sudoku. Being great brothers, John picks-up on that and proposes that they instead make their own sudoku, based on their game. They sit together and joyfully come up with the rules and starting grid for their new creation, Tic-Tac-Toe Sudoku.

Rules. I must underline that the story does include clues that are needed during the solve.

1. Each 3x3 sudoku box is a tic tac toe box. It can contain an X, O, or nothing. The solved grid must be a valid tic tac toe grid.

2. The content of a box is determined by the upper-left cell, the start of the symbol, and the make-up of the box. If a box starts with one of 5 specified digits it’s an X or an empty box (neither X nor O) if it isn’t a valid X shape. If a box starts with one of 4 specified digits it’s an O or an empty box (neither X nor O) if it isn’t a valid O shape.

3. John’s Xs are always perfect, there is only one way to make an X. Michael’s Os aren’t always perfect (he’s still learning how to write), there is one way to make a perfect O, but multiple ways to make valid Os. They notice that if Michael manages to get to the upper-right corner he makes a perfect O (this means that having deduced a box can’t be empty, if an O digit is found in the upper-right corner, the box must be a perfect O). He did this twice. They also realize that no Os cross the center of the box and that in imperfect Os, each cell must contain at least an orthogonally adjacent sibling. Example (note: invalid Xs and invalid Os can also be considered empty/invalid boxes, they are shown to better explain the different make-ups of Xs and Os)

4. For this puzzle, Xs are made up entirely of prime digits (1,2,3,5,7) and Os are made up of composite digits (4,6,8,9)

5. Normal sudoku rules apply

6. Digits along the thermometer must increase from bulb to end

7. The inequality sign shows which digit is greater

8. The little killer clue is a prime number, the digits on that diagonal sum up to a prime number

9. The killer cages sum up to a prime number. If we were to remove the last cell (bottom for vertical cages, right for horizontal cages), the remaining cage would still sum up to a prime number. We can repeat this as many times as the cage allows. Example: 3,4,6 is a valid killer cage, 3, 7, 13 are all prime; 3,6,4 and 4,3,6 are not valid as 9 respectively 4 are not prime

10. All 3 digit clues must include a 2

11. Each X must start with a different digit

12. Each O must start with a different digit