This Impossible Game Makes NO Sense

August 2, 2020



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Conway Checkers (proof), Numberphile2 | Zvezdelina Stankova:

Conway’s Soldiers Interactive Game (Clever Learning):

John Conway’s work stretched from nearly-inaccessible math theory to fun children’s games, and it defined how we thought about recreational mathematics in the 20th century. Conway’s Soldiers is the perfect example of a Conway-esque math game: the rules are simple, the gameplay is easy, and it becomes very hard very quickly… and in this case of a basic checkers game, it packs a surprising punch of becoming literally impossible for a reason that isn’t even close to obvious.

But the mathematical importance doesn’t end with an unexpected reveal of impossibility. Conway found that the secret to *why* it’s impossible depends on the Golden Ratio of 1.618, which has fascinated mathematicians since Pythagoras and Euclid. We see the Golden Ratio in aesthetically-pleasing magazine layouts, flower patterns, and pretty faces, but John Conway showed us that it’s at the heart of why we can’t reach the fifth row of a checker game.

Play the game yourself with the online simulator and check out Zvezdelina Stankova’s proof on Numberphile. It’ll make sense. John Conway may be gone now, but we’ll be playing his games and poring over his ideas for centuries.

*** SOURCES ***

Berlekamp, E. R.; Conway, J. H; and Guy, R. K. “The Solitaire Army.” In Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, pp. 715-717 and 729, 1982.

Honsberger, Ross. “A Problem in Checker Jumping.” Ch. 3 in Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 23-28, 1976.

Tatham, Simon and Taylor, Gareth. “Reaching Row Five in Solitaire Army.”

plus magazine, “Mathematical Mysteries: The Solitaire Advance.”

Bell, George. “The Peg Solitaire Army.”

Bell, Hirschberg, Guerrero-Garcia. “The Minimum Size Required of a Solitaire Army.”

Taylor, Jasper. “Conway’s Soldiers.”

John Conway’s obituary, New York Times:

Roberts, Siobhan. “Genius at Play: The Curious Mind of John Horton Conway” (2015).

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All Comments

  • I created my own game I don't know the name but it's really easy to play but really hard too win

    TWB studio August 2, 2020 9:29 am Reply
  • fk fk

    ray lopez August 2, 2020 9:29 am Reply
  • Kevin vsause here

    marijan ešegović August 2, 2020 9:29 am Reply
  • "get ready to social distance your heart out"

    me: that aged well

    then i see upload date

    me: oh

    racecraftr August 2, 2020 9:29 am Reply
  • Was I the only one who didn’t know that solitaire wasn’t JUST the card game?

    Pretty Bird29 August 2, 2020 9:29 am Reply
  • give this problem to an AI and let it run for a month or two unsupervised

    d3monshadow August 2, 2020 9:29 am Reply
  • "It’s like trying to invade Russia in winter"
    Actually literally everybody invaded in summer, but fought until winter.
    Забавно 😀

    Александр Шахов August 2, 2020 9:29 am Reply
  • That ending is beautiful ; ~ ;

    Cyan Griffin August 2, 2020 9:29 am Reply
  • This man is CEO of “Right? WRONG!”

    Elsa Rieben August 2, 2020 9:29 am Reply
  • 9:50 is that a jojo reference on stell ball run

    I fish that Johnny joestar eat August 2, 2020 9:29 am Reply
  • wheres the link

    The crazy Lewises August 2, 2020 9:29 am Reply
  • Social distance, heh.

    Clan Survival Server August 2, 2020 9:29 am Reply
  • Whats with his right, wrong all the time. At first it was a bit of an jumpscare when he said it

    Siptom August 2, 2020 9:29 am Reply
  • if you are allowed to jump diagonally you can get someone to row 5 with 14 checkers

    sebastianrchase8989 August 2, 2020 9:29 am Reply
  • Could you do it if you could move diagonally?

    The Ninth Pringle August 2, 2020 9:29 am Reply
  • “It’s like trying to invade Russia in winter…” “…Impossible.”

    Selim Topal August 2, 2020 9:29 am Reply
  • idk i drew a board 10 pages long and i got pretty close i had one on 4 and one on 2

    Bob li August 2, 2020 9:29 am Reply
  • My friend beat it and idk how

    Luke Requejo August 2, 2020 9:29 am Reply
  • My life is solitaire

    Hahaaaaaaaaaaa depression fuuuuuunnnnny

    Water Sheep August 2, 2020 9:29 am Reply
  • 9:16

    IsaacRoan Sison August 2, 2020 9:29 am Reply
  • The maths were thought by god ti be these… To be beautiful… Vsauce. . incredible

    Solo llámame Diego August 2, 2020 9:29 am Reply
  • Extend our Vsauce t(w)o empire

    1ce_s0n1c August 2, 2020 9:29 am Reply
  • Well, the title was right. This made no sense.

    Mr. Duckford August 2, 2020 9:29 am Reply
  • You could've just said that moves is 2^n – 1

    Anything Anyway August 2, 2020 9:29 am Reply
  • There is a solution to level 5….

    Sean Jeremy Henry Sihombing August 2, 2020 9:29 am Reply
  • “Not my thing “

    Adeeb Gaming August 2, 2020 9:29 am Reply
  • Why do you never explain it in the end, it’s frustrating and confusing…

    Ronikun August 2, 2020 9:29 am Reply
  • I did it

    WhiteHairBoy Kun August 2, 2020 9:29 am Reply
  • The board you linked to isnt big enought, but theoretically, given an infinintly long 5 wide space, you can get any distance Ill try to make a visual proof, but i believe I have found the solution

    Lizzard Doggo August 2, 2020 9:29 am Reply
  • It's possible to invade Russia during winter, just not from the west

    Anamosa Mapper August 2, 2020 9:29 am Reply

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