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A pair of Find-the-stars puzzles Question
Find-the-stars instructions:
A Find-the-stars puzzle is played on a square grid that is initially empty except some squares contain arrows.
The goal of the puzzle is to fill some empty squares with stars so that:
- Every row contains exactly one star.
- Every column contains exactly one star.
- Stars are NOT placed in squares that contain an arrow.
- If a square contains a SOLID arrow, THEN exactly one square in the direction of the arrow will contain a star.
- If a square contains a DASHED arrow, THEN none of the squares in the direction of the arrow will contain a star.
Warmup puzzle:
Warmup solution:
Spoiler! Click here to reveal warmup solution
Main puzzle:
1 answer
Spoiler
The answer is:- - - - - - - - X - 10 - - - - - - X - - - 9 - - - X - - - - - - 8 X - - - - - 7 - - - - X - - - 6 - - - - - X - - 5 - - X - - - 4 - - - - X - - - - - 3 - - - - - - - - - X 2 - X - - - - - - - - 1 1 2 3 4 5 6 7 8 9 10
To solve this puzzle, we mark the initial conditions. For simplicity of typing, I'll use ASCII art with the following meaning:
"-" unresolved square
"O" resolved empty square
"X" resolved marked square
"+" contains a dashed arrow, resolved empty
"ul" "ur" "ll" "lr" arrows pointing to upper/lower left/right
I'll also number the rows and columns to make individual squares easy to talk about.
The initial conditions are:
- - - O - - O - - - 10 - - - - O O - - - - 9 - - - - O O - - - - 8 - - - + ul ur + - - - 7 O O O + - - lr - - - 6 - - - ll - - lr - - - 5 - - - lr ll + + - - - 4 - - - - - O O - - - 3 - - - - - O O - - - 2 - - - - - O O - - - 1 1 2 3 4 5 6 7 8 9 10
Due to the LR arrow at 4,4, 5,3 must be marked. Whenever we mark a square, we cross out all other squares in that row and column. This gets us:
- - - O O - O - - - 10 - - - - O O - - - - 9 - - - - O O - - - - 8 - - - + ul ur + - - - 7 O O O + O - lr - - - 6 - - - ll O - lr - - - 5 - - - lr ll + + - - - 4 O O O O X O O O O O 3 - - - - O O O - - - 2 - - - - O O O - - - 1 1 2 3 4 5 6 7 8 9 10
Nothing is immediately forced from this position, but there are several places where there are only two options. For example, the LR arrow at 7,5 means one of 8,4 and 10,2 must be marked.
However, if we mark 8,4, then the arrow at 7,6 can't be satisfied. That means we must mark 10,2:
- - - O O - O - - O 10 - - - - O O - - - O 9 - - - - O O - - - O 8 - - - + ul ur + - - O 7 O O O + O - lr - - O 6 - - - ll O - lr - - O 5 - - - lr ll + + - - O 4 O O O O X O O O O O 3 O O O O O O O O O X 2 - - - - O O O - - O 1 1 2 3 4 5 6 7 8 9 10
From this point, there are no more guesses required. At each position, there is at least one forced square. In this position, 8,4 is forced since that's the only option to satisfy the arrow at 7,5.
I'm not going to show each of the resulting positions since the remainder of the puzzle is just filling in forced squares.
If you keep going, you end up with the solution I posted above. In this whole process, we only had one choice with two possible moves, and one of them turned out to not work. Therefore, we know this is the only possible solution.
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