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#### Arrows

##### (Eggleton & Fraenkel, 1975)

Categorize 9 games based on the answer to two questions:

1) Will Emperor Jiaqing win / tie / lose if he goes the first.

2) Will the Pirate, Ching Shih, win / tie / lose if she goes the first.

The games are all variants of the game “arrows.” This is a great logic puzzle and the combination with the overarching sorting question makes this activity a big winner.

Get the 9 printable game-sheets here.

* These games are based on the 1975 game Arrows. That game was played on a grid with 25 spaces – seven pieces per player. These simpler games are meant to be “solved” by young students. What do I mean by “solving” a pure strategy game? I mean that if two good thinkers play one of these games, the outcome of the game is a forgone conclusion. Tic Tac Toe is solved. The first player always wins. If chess was solved it may turn out that the game is always a tie between sufficiently godly players. The other options would be that chess is always won by the first godly player (white) – or is always won by the second godly player (black). We are not gods – that’s the only reason that chess is still interesting. We have not solved it. Intelligent gods would find chess boring.

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

G. H. Hardy

#### Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

##### MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

##### MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

##### MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.