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Here is one possible way of generating all 12 solutions by 2x2x3 choices: 1. Fill the upper left box with 1-2-3-4 2. Choose where to put the 1 in the top righ
by antonTobi 18d ago
Here is one possible way of generating all 12 solutions by 2x2x3 choices:
1. Fill the upper left box with 1-2-3-4
2. Choose where to put the 1 in the top right box (2 choices)
3. Choose where to put the 1 in the lower left box (2 choices)
4. Choose which digit to put diagonally opposite the 1 in the lower right box (3 choices)
Is there a nicer way which makes it obvious that there is exactly one solution for each choice in the last step?
- Someone 18d ago> Choose which digit to put diagonally opposite the 1 in the lower right box (3 choices) There are only two choices there. You cannot put a 1, nor the digit (3 or 4) that’s in the top the column where you try to put the number. > Is there a nicer way which makes it obvious that there is exactly one solution for each choice in the last step? There isn’t. You may end up with a degree of freedom after step 4 1234 1234 ..1. ..1. ...1 ...1 .1.. .14. leads to 1234 ..12 ..21 2143 which allows for 2 solutions: 1234 1234 3412 4312 4321 3421 2143 2143
- antonTobi 18d agoMy procedure starts with filling the top-left box, not the top row. So it looks something like this after the third step: 12.. 34.1 .1.x ..1. From here x can be any of [2,3,4], and each yields exactly one solution!