Season 2 • Episode 18 • Sprouts

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Season 2 • Episode 18 • Sprouts

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Sprouts

Season 2

Episode 18 Time frame 2 periods

Objectives :

•

^Introdue ^the ^voabulary^of ^Graph ^theory.

•

^Show^how ^a ^game^an ^be^solved ^by exhaustion.

Materials :

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^Rules.

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^A ^large ^room, ^with ^not ^too ^many ^tables ^and ^hairs, ^would ^be ^better ^suited

for this ativity.

Period 1

1 – The rules of the game 10 mins

Therules ofthegameareexplained,withafewgamesplayed ontheboardbythe teaher

and some students.Voabulary is introdued.

Graph Vertex Edge Order of agraph Degree of avertex

2 – Playtime ^{10 mins}

Students play some game of sprouts by pairs.

3 – Solving the 1-vertex game 5 mins

The 1-vertex game is ompletelysolved and itis shown that it's aseond-playerwin.

4 – Solving the 2-vertices game 30 mins

Students have to olletively solvethe 2-verties game and nd out if there is a winning

strategy. Teaher's inputshould beminimalduring this part.

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^The ^lass ^is ^divided ⁱⁿ^four ^groups.

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Êah ^groupîs ^given ^some ^large ^paper^sheets ^(half^lip-board ^sheets) ând ^some ^pens.

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Êah ^group^has ^to ^buildâ ^large ^tree ^showing âll^the ^possible ^moves, ^with ône ^moveôn

eah paper. Equivalent movesmust not be dierentiated.

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Êah ^group^has ^to^devise â ^winning^strategy ^for ^the ^rst ôr ^seond ^player.

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Season 2 • Episode 18 • Sprouts

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Period 2

5 – Solving the 2-vertices game (continued) 10 mins

Students are given some time to take a look at the tree they did during the previous

periodand review the winning strategy.

6 – Championship 35 mins

Eah group plays a 2-verties game against every other group twie (swithing rst and

seond players ineah game).

G1 G2 G3 G4

G1

G2

G3

G4

A mark isthen awarded tothe group dependingon the number of wins :

1 win : 12 points;

2 wins : 15points;

3 wins : 18points;

4 wins : 19points;

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Sprouts

Season 2 Episode 18 Document Rules

1 Origin and rules

The game alled Sprouts was reated in 1967 by mathematiians Mihael S. Paterson

and John H. Conway (the reatorof the gameof Life).

This is a two-players game, played with just penil and paper. Start with a number of

spots,orverties.Thetwoplayerstaketurnsdrawingaline(notforedlystraight)between

twoverties orfromavertex toitself, andplaing anew pointon the line.A turn isalso

alled a move. A few rules apply :

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Â ^line^must ^not ^ross âny ôther ^line.

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Ât ^most ^three ^lines ân ^start ^from âny ^vertex. ^We ^say ^that êah ^vertex ^has êxatly

three lives. When exatlythree lines start from one vertex, it is onsidered dead and

annot be used inthe game any longer.

Season 2 • Episode 18 • Sprouts