Solidarity – Poland, 1981

This game is a blend of strategy and deception. You start the game by being randomly dealt one of five cards (Communists, Nobility, Farmers, Clergy, Workers.)



You secretly draw the Clergy. You want the Clergy to win. For your first turn you connect two hexagons.

Your enemy secretly draws Communists. You do not know this. They make two connections.

The lower group is currently worth three points because it consists of three hexagons. These points are currently going to green Farmers because there are more green Farmers than anything else. The upper group is worth two points. Orange Nobility and green Farmers are tied. In the case of a tie the color highest up the list on the left wins (Communists > Nobility > Farmers > Clergy > Workers). That means the orange Nobility is currently worth two points.

Unfortunately for green and orange – points are computed at the end of the game – not right now.

You do not want to be too obvious so you pretend to help the green Farmers. You add three connectors. Each connector added must connect at least one new hexagon.

Before the game begins decide how high you are going to go before players stop increasing the number of connectors placed on a turn. On the first turn we placed 1, on the second 2, on the third 3. You must stop increasing at 3, 4 or 5 connectors. In this game we decided on 4.

Your enemy makes four connections. From now on players may make four connections every turn.

If the game was to end right now who would win? The big group of connected 6 hexagons on the right have more green farmers than anything else – so green would get 6 points. The second biggest group of two blues and a gray gives 3 points to blue. Who wins the little green-orange couple on the left? It seems tied. In the case of a tie look at the hierarchy on the left of Poland. Red communists are on top. The higher one wins in a tie. Orange is higher than geen so orange wins. Do this for all groups and add up the results. The highest wins, but don’t do this now – wait until there are no moves left.


Oops – we made a mistake placing. The red connection is wrong because both hexagons have previously been visited. Remember – every connection must visit at least one previously unvisited hexagon.

Let’s choose to do something different.

Now we pretend to help the Workers.

The enemy is being irritating. You still do not really know what color they are.

You have decided to make a move that tells your opponent that you are blue. If the game ended right now – that big group (9 points) would be yours (there are three blue and three gray, but blue is higher.)

The opponent now guesses that we are the blue Clergy. We still do not know if they are the Communists, Nobility or Farmers. They don’t look like they are the Workers.

Let’s pretend we are gray.

It looks like our opponent is the red Communists.

We can get more blue Clergy points.

Red Communists are definitely our opponents.

The final connections… and now it is time to score.

Before scoring it is worthwhile to noticing that the breaking-tie advantages of those high on the list (Communists > Nobility > Farmers > Clergy > Workers) is balanced because there are more hexagons of those near the bottom of the list (Communists (10) < Nobility (11) < Farmers (12) < Clergy (13) < Workers (14)).


Drats. The Communists have won. Red Communists (21), Orange Nobility (2), Green Farmers (13), Blue Clergy (13), Gray Workers (11). We Clergy tied for second place with the Farmers.



Hope you enjoy this game whilst remembering the heroic times of Solidarity.


The game can be played with different maps…


If the cities of Warsaw and Gdansk are labeled on a map – any group that includes at least one of these cities has its score doubled.

Download a pdf of some game boards and cards here.

Solidarity – Poland, 1981

(Gordon Hamilton [Dr. Pickle], 1993)

This game of deception and strategy is a great way to get students to count, add, and think about hierarchies. Most children aged 7 will not be able to play the game effectively by themselves, but it is good to match half the class against the other half.

Download the pdf file here.

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 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

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)