All Questions
Tagged with lights-out combinatorics
8
questions
2
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0
answers
89
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An array of light-bulbs [duplicate]
There is a grid of 2024 by 2024 light-bulbs. Initially, all bulbs are off.
You can switch the state of all 2024 bulbs in a row simultaneously, or all 2024 bulbs in a column simultaneously, and do this ...
12
votes
4
answers
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Prime lights out
You start with a 4x4 grid filled with zeroes. If you press a cell then the cell and all its neighboring (horizontally and vertically) cells will have their numbers increased by 1. What is the most ...
- 36.3k
6
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3
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Flipping coins in a circle
We have a set of N coins that are all placed in a circle. They all have "Tails" as their face up side. The coins are all distinct and have numbers (1,2,3...N) written on them.
In each move, ...
- 3,373
5
votes
2
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Highest n where an equal number in all cells is (im)possible
Inspired by Board with all 2020s :
Zeroes are written in all cells of a n×n board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it.
...
- 9,366
6
votes
3
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Different numbers in all cells of a 4x4 board
This is a harder version of this puzzle: Different numbers in all cells of a 3x3 board
Zeroes are written in all cells of a 4×4 board. Pressing a cell increases by 1 the number in this cell and all ...
- 36.3k
6
votes
2
answers
483
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Different numbers in all cells of a 3x3 board
This puzzle is inspired by this one: Board with all 2020s
Zeroes are written in all cells of a 3×3 board. Pressing a cell increases by 1 the number in this cell and all cells having a common side with ...
- 36.3k
18
votes
5
answers
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Board with all 2020s
Zeroes are written in all cells of a $5 \times 5$ board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it. Is it possible to obtain ...
- 890
5
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3
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Will you be the first to get free?
It is your first day in prison and you are approached by a guard having a hunch for puzzles.
He tells you that he gives every new prisoner the chance to be freed if they can present him with a version ...
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