The Dollar Game

A graph-based single-player game inspired by one Numberphile video.

Description

A given game is represented by a connected graph consisting of nodes (people) and edges (connections).
Let two people having a connection be called neigbours. Each node (person) in this network has a value (some integer amount of money).

Actions

Every person can perform two actions:

• give: reduce its own value by a number of its neighbours and increase each of those neigbours' values by one;
• take: vice versa.

Objective

By executing a sequence of actions with the least possible length distribute money in the network in such a way that no person has debt (a negative value).

Tutorial

Game mode

Note: has orange outline outline when the game is in progress and green outline in case of the victory.

This window has two regions: the one with the indicators and the second with the game itself (boxed in a thin light blue rectangle).

As is was mentioned above, the game is represented by a graph with people as nodes and connections between them as edges. A number to the south-east of a node shows its value (red if it is negative and white otherwise). By hovering a node and scrolling up/down one can execute the give/take action on this node. Also, you can perform these actions using the keyboards: type a node's index number and press UP to give or DOWN to take.

Outside of the game field there are:

• GENUS: [pararmeter] $E-N+1$, where $E$ and $N$ are the number of edges and nodes respectively (we will need it later);
• BANK: [parameter] simply the sum of all values;
• MOVES: [counter] the number of moves executed by the player so far;
• Best: [] (is shown only if the game has been played before) the least number of moves which led to the victory;
• Save: [button] saves the game to the disk (also saves the sequence of moves if pressed after winning)

Hint: hit RETURN to solve the game algorithmically.

Sandbox mode

Note: has magenta outline.

The game can be created inside of the thin light blue rectangle. Click an empty region to create a node, use your mousewheel while hovering a node to change the latter's value. Left click and hold a node, then release on the other node to create an edge. You can also delete nodes and edges by repeating the corresponding action.

Options window

Note: has limeish outline.

Here you can configure some of the game's parameters such as:

• indices [boolean]: whether to display nodes' indices when playing or creating (may be of help when requesting and examining the solutions);
• best [boolean]: whether to give an option to peak the solution calculated by the algorithm when playing (note:when this is on some complicated games may take more time to load);
• sortby [one of a list]: choose a parameter to sort games in the OpenWindow with;
• layout [one of a list]: choose a layout in which newly generated games will be drawn.

There is also a command line providing functionality to delete, reset, change the existing games or get in-depth statistics on them. Try 'help' to learn more.

Open window

You will see the table of green panels which show games' information: number, an amount of nodes and edges and how many times they have been solved before; moreover, the best of those solutions is shown (measured by the number of moves: fewer is better). Scroll the mousewheel or use the 'u'/'d' buttons to navigate. When hovering a panel hold shift to glimpse a preview of the game. Click a panel to proceed.

Alternatively, one can open a game by typing its number using a keyboard and pressing RETURN.