How to solve Minesweeper In 3 minutes Steven Waterman LOOK HERE IF - - PowerPoint PPT Presentation

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How to solve Minesweeper In 3 minutes Steven Waterman LOOK HERE IF - - PowerPoint PPT Presentation

Oct 16, 2023 259 likes •847 views

How to solve Minesweeper In 3 minutes Steven Waterman LOOK HERE IF YOUVE PLAYED MINESWEEPER BEFORE LOOK HERE IF Basics YOU DONT KNOW WHAT MINESWEEPER IS Minesweeper Board! Rectangular! Cells! Cells can be clear or mines 1 2 1

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SLIDE 1

How to solve Minesweeper In 3 minutes

Steven Waterman

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SLIDE 2

Basics

LOOK HERE IF YOU’VE PLAYED MINESWEEPER BEFORE LOOK HERE IF YOU DON’T KNOW WHAT MINESWEEPER IS

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SLIDE 3

Minesweeper Board!

Rectangular! Cells!

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Cells can be clear or mines

1 2 1 2 1 2 2 2 2 2 2 1 1 2 2 2 1 1 2 2 2 1 1 1 1 1 2 1 1 1 2 3 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 2 2 1

There is 1 mine in these 3 cells

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SLIDE 5

Let’s Play!

9x9 board, 15 bombs

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SLIDE 6
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1 1 1 1 1 2 2 1 1 1

2 mines / 2 unknowns All are mines Can flag

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1 1 1 1 1 2 2 1 1 1

0 / 2 None are mines Can Clear 0 / 3 None are mines Can Clear

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1 1 1 1 2 1 3 1 2 2 3 1 3 1 1

1 / 1 Can Flag

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1 1 1 1 2 1 3 1 2 2 3 1 3 1 1

0 / 2 Can Clear 0 / 1 Can Clear

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1 1 1 1 1 2 3 1 3 1 2 2 3 1 3 1 1 2

Stuck :(

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1 1 1 1 1 2 3 1 3 1 2 2 3 1 3 1 1 2

1 / 5 1 / 2

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1 1 1 1 1 2 3 1 3 1 2 2 3 1 3 1 1 2

1 / 5 1 / 2 Contains

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SLIDE 14

1 1 1 1 1 2 3 1 3 1 2 2 3 1 3 1 1 2

0 / 3 Can Clear 1 / 5 1 / 2 minus 1-1 mines 5-2 cells 0 / 3

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2 1 2 1 1 1 1 1 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

2 / 2 Can Flag 1 / 1 Can Flag

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2 1 2 1 1 1 1 1 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear

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SLIDE 17

2 1 2 2 1 1 1 1 1 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear

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2 2 1 2 2 1 1 1 1 1 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

1 / 3 1 / 2 Contains

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SLIDE 19

2 2 1 2 2 1 1 1 1 1 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear 1 / 3 1 / 2 Contains

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SLIDE 20

2 2 1 2 2 1 1 1 1 1 2 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

1 / 5 1 / 2 Contains

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SLIDE 21

2 2 1 2 2 1 1 1 1 1 2 2 1 2 3 1 3 1 2 2 3 1 3 1 1 2

0 / 3 Can Clear 1 / 5 1 / 2 Contains

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SLIDE 22

2 2 1 2 2 1 1 1 1 1 1 2 2 1 1 2 3 1 1 3 1 2 2 3 1 3 1 1 2

1 / 5 1 / 2 Contains

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SLIDE 23

2 2 1 2 2 1 1 1 1 1 1 2 2 1 1 2 3 1 1 3 1 2 2 3 1 3 1 1 2

0 / 3 Can Clear 1 / 5 1 / 2 Contains

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SLIDE 24

2 2 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

1 / 4 1 / 2 Contains

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SLIDE 25

2 2 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

0 / 2 Can Clear 1 / 4 1 / 2 Contains

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SLIDE 26

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

1 / 3 1 / 2 Contains

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SLIDE 27

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

0 / 2 Can Clear 1 / 3 1 / 2 Contains

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SLIDE 28

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

2 / 3 1 / 2 Contains

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2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

1 / 1 Can Flag 2 / 3 1 / 2 Contains

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SLIDE 30

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

1 / 3 1 / 2 Contains

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SLIDE 31

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 1 2 1 3 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear 1 / 3 1 / 2 Contains

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SLIDE 32

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 1 2 2 3 1 3 1 1 2

1 / 3 1 / 2 Contains

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SLIDE 33

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear

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SLIDE 34

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

1 / 1 Can Flag

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SLIDE 35

2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

0 / 1 Can Clear

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SLIDE 36

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

Stuck :(

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SLIDE 37

Let’s Play!

9x9 board, 15 bombs

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Let’s Play!

9x9 board, 15 bombs

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Let’s Play!

9x9 board, 15 bombs

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Let’s Play!

9x9 board, 15 bombs

15 bombs 15 bombs 15 bombs 15 bombs 15 bombs

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

15 / 81

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

7 / 20

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

6 / 18

1

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

5 / 18

1

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

4 / 18

1

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2 4

0 / 18

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SLIDE 47

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 1 1 2

0 / 9 Can Clear

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SLIDE 48

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 3 2 2 1 2 1 2 1

2 / 2 Can Flag

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SLIDE 49

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 1 3 3 2 2 1 2 1 2 1

0 / 1 Can Clear

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SLIDE 50

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 1

2 / 2 Can Flag

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SLIDE 51

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 1

0 / 1 Can Clear

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 1

1 / 1 Can Flag

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 1

0 / 1 Can Clear

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 2 1

...What now? It’s time for...

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SLIDE 56

2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 2 1

Guessing

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2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 2 3 2 1 2 1 3 3 4 1 2 2 3 4 1 3 3 2 2 1 2 1 2 2 1

:(

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SLIDE 58

Next time:

  • Constraint Reduction
  • Inexact Constraints
  • Proof of Completeness
  • How to actually implement it
  • How to do it without taking exponential time

So get excited for How to solve minesweeper in a series of 20 hour-long lectures! (bad solver code on github @stevenwaterman)