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# Season 2 • Episode 18 • Sprouts

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## Sprouts

### •

Introdue the voabularyof Graph theory.

### •

Showhow a gamean besolved by exhaustion.

Rules.

### •

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

for this ativity.

## 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.

### •

The lass is divided infour groups.

### •

Eah groupis given some large papersheets (halflip-board sheets) and some pens.

### •

Eah grouphas to builda large tree showing allthe possible moves, with one moveon

eah paper. Equivalent movesmust not be dierentiated.

### •

Eah grouphas todevise a winningstrategy for the rst or seond player.

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1

## 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 :

### •

A linemust not ross any other line.

### •

At most three lines an start from any vertex. We say that eah vertex has exatly

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

annot be used inthe game any longer.

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