(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.

Steve Heller has created a beautiful Jamboard version 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!

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

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Use the right tools!

Students should use the right tools: 0-99 wall charts, graph paper, etc.

MP6 Be precise!

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!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)