Seven Bridges Rulebook

Table of Contents

Table of Contents

• Overview
• Components
• Setup
• How to Play
  • Drafting
  • Get on Your Horse!
• Visiting Landmarks
  • Immediate Use
  • Reserved Use
• Scoring
  • Total Score
  • Variant: Committed Scoring
• Now, Where Were We?
• Rules for Solo Play
  • Drafting
  • Scoring
  • Solo Difficulty
• About the Map

Overview

1 to 6 players, 15-20 minutes per player, ages 10+.

Components

• First-player marker
• Wooden dice (6)
• Pencils (6) with holder
• Eraser
• Player map pad (100 double-sided sheets)

Each wooden die has six faces, each printed with one of six line shapes: a 3 die (a straight line three map squares long), a + die (a four-way crossing), a T die (a three-way branch), an I die (a straight line one map square long), an L die (a right-angle corner), and a blank/dot die (a short line with no direction of its own). Two of the map pad's printed columns also show a 2 die (a straight line two map squares long) and a 3 die as landmark bonuses; see Visiting Landmarks.

Setup

Hand out a map and a pencil to each player. Give the first-player marker and the dice to the person who most recently crossed over a bridge. If no one can recall having crossed a bridge recently, use another method to choose the first player.

There are thirty spaces along the bottom edge of the map that can be used to track the game's progress. Each of the five rounds has six spaces, one for each possible player. Before starting, cross out the spaces that won't be needed: in a four-player game, everyone can cross out the first two spaces in each round.

Next, decide where players will begin exploring the city of Königsberg. Everyone starts the game in the same place, so choose any square that has streets and/or footpaths inside it and color them in.

If there are any footpaths or landmark identifiers in the starting square, see Visiting Landmarks.

Alternatively, you can roll three dice to decide where the game will begin. Each face corresponds to a value from 1 to 6 as shown in the IMMEDIATE USE column to the left of the map. The first roll determines the quadrant (i, ii, iii or iv; re-roll a 5 or 6), the second roll determines the row in that quadrant, and the third roll determines the column. If there aren't any streets or footpaths in that square, select an adjacent one.

If there is a landmark identifier in the game's starting square, all players get to choose a bonus immediately (before the dice are rolled for the first time).

If there are any footpaths in the game's starting square, everyone should immediately color in this bonus and its triangle - all players are allowed to draw lines on footpaths throughout this game.

How to Play

Please note that these instructions use the terms die (singular) and dice (plural).

Players perform two kinds of drafting in this game: dice drafting and map drafting. First you draft (choose) a die, then you draft (draw) its lines onto your map!

The first player rolls all six dice. Starting with this player and continuing clockwise until the sixth die has been drafted, each player chooses one die to immediately add to their map.

When playing with two, three or six people, each player will draft the same quantity of dice per turn. With four or five people, the quantity of dice each player drafts per turn will vary.

Regardless of how many people are playing, a game lasts five rounds and each player will always draft six dice per round and thirty dice per game.

Drafting

There are several rules that must be followed when drafting a die:

• Connectivity: New lines must connect to your existing network of lines in at least one spot.
• Extremity: At least one end point of new lines must connect to your existing network. End points are only found at the edges of dice, except for the I die, which also has an end point in the center.
• Totality: You must be able to add all the lines on the chosen die to your map. In our example from the previous page, no one can choose a + die at the beginning of the game because there aren't any adjacent squares in which it can be drawn (see Downgrade below).
• Exclusivity: Lines from one die can be added to only one square on the map, unless you choose a 2 or 3 die (see Get on Your Horse! below).

Exclusivity: Be careful when drafting an I die: it can only be added to one map square.

• Continuity: If you draft multiple dice during the same turn, you must add the lines to your map in the order that the dice were chosen. To ensure this, the next player does not have to draft their die until you have drawn the lines on your current die.
• Backtracking: You can add new lines to a previously-visited map square, but you can never draw on top of previously drawn lines. Crossing over (perpendicular to) a drawn line is permitted.
• Footpaths: You cannot draw on the dashed lines on the map until you have reserved the footpath bonus from the RESERVED USE column (see Visiting Landmarks).
• Downgrade: If you are unable to continue your exploration of the city because none of the available dice can be added to your map, you may downgrade one of them. You cannot downgrade if there are any 2 or 3 dice available (see Get on Your Horse!). Referring to the IMMEDIATE USE column to the left of the map, take the die with the lowest numerical value. Increase its value by one by physically turning it over to the next side shown in the diagram. Keep doing so until the die fits anywhere on your map, and as soon as it does, you must use it.

In our example, this player was able to draft two dice in the first turn: a 3 which they added to the left of the starting square, and an L which they added above. If any player had been forced to draft a + as their first die, they would have to downgrade it to a T before they could use it.

With the first turn of the first round complete, the player has filled in a space on the turn tracker.

Exclusivity and Connectivity: If this player were to draft an I die next, it could only be added horizontally to the left or to the right of their existing lines.

When the final die of the turn has been drafted, all six dice are passed clockwise to the next player and a new turn begins. At the end of the last player's turn, the round ends. Pass the first-player marker clockwise to the next player, and start another round.

Get on Your Horse!

If you choose a 2 or 3 die, you can draw a straight line up to two or three map squares in length! This line can be connected to your existing network anywhere except at a right angle to straight segments. In these locations, only 2 or 3 dice can be drawn!

• The new line cannot bend or be divided into multiple parts.
• The new line can start and/or finish in the middle of a map square.
• The new line can be added at a right angle to an end point in the middle of a map square (see the square directly above bridge #1).

Most importantly, you may draw a line shorter than two or three squares in length. For example, if you choose a 2 die, you can draw a line measuring two map squares, one and a half squares, one square, or just half a square in length. This flexibility allows you to:

• Draw a line exactly to the edge of your map.
• Stop the line where you think it might be convenient to do so.
• Draft one of these dice, rather than downgrading.

Examples of where the lines on a 3 die can and cannot be drawn.

Visiting Landmarks

There are eleven landmarks on the map, labeled A through K. Whenever you identify a landmark – by drawing a line that passes in front of its letter – you get to select a bonus from either the IMMEDIATE USE or RESERVED USE column to the left of the map. Each bonus can be used only once.

Immediate Use

As its name suggests, when you choose a bonus from this column, it is applied immediately. Select the bonus die that you want to use and add its lines to your map, following the same rules outlined earlier in the Drafting section. Bonuses can be rotated, just like dice.

Once you have drawn your bonus lines, color in both the symbol and the triangle of that bonus to show that it has been used. You may be able to visit several landmarks at once by chaining bonuses together!

The IMMEDIATE USE column lists seven bonus dice, each worth the usage-bonus value printed beside it: a 3 die (value 1), a + die (value 2), a T die (value 3), an I die (value 4), an L die (value 5), a blank/dot die (value 6), and, listed separately, a 2 die (value 1).

Reserved Use

When selecting a bonus from this column, color in the symbol but not the triangle beside it. Starting with the next time that you draft a die, you may opt to use this bonus. When you decide to use it, then and only then should you color in the triangle.

If you reserved the footpaths bonus, then you can start drawing lines on footpaths. The first time that you do so, color in the triangle next to this bonus.

If you reserved a re-roll/distribute bonus, then when it's your turn to draft a die you may either:

a) Re-roll all the available dice before drafting your die. The game then continues normally, using the remaining re-rolled dice. Players may re-roll or distribute dice later during this same turn, using one of their own reserved bonuses.

b) Distribute all available dice as you see fit, taking care to give the correct number of dice to yourself and each other player. Use this bonus to take exactly the dice that you want, and pass less desirable dice to your opponents! These players, however, may re-roll the dice they were given (if they have a bonus reserved and wish to use it). If you receive more than one die, ignore the Continuity rule - you may add the dice to your map in any order (obeying the other Drafting rules, of course).

You must select and use the three re-roll/distribute bonuses from top to bottom as shown in the RESERVED USE column. You do not, however, have to use a bonus before reserving another.

When drafting a die, you can use one re-roll/distribute bonus: you cannot re-roll the same dice twice, or re-roll dice and then distribute them. You can, however, use more than one bonus per turn if you draft dice more than once that turn.

Scoring

There are seven different ways to score points, one for each item in the map's legend. If possible, use a different color for your scoring: it will stand out from the lines already drawn on your map, and it looks nice!

Our player's finished map, before calculating their score. Note that they reserved the footpath bonus but did not use it and that they colored in the seven landmark identifiers that they passed in front of. The smaller rectangles in the map legend are used to record Euler's score (see Rules for Solo Play).

1. Street; footpath - If you drew any closed loops on your map, find the one that will score you the most points: multiply the number of corners (right angles) that it has by the number of bridges that it crosses. A closed loop that doesn't cross any bridges does not earn a multiplier; simply count the number of right angles it has.

   Our player found a closed loop with twelve corners that crossed three bridges, earning 36 points. There are several closed loops on the map, but this is the highest scoring. As in this example, the largest loop may not be the one that earns the most points.

2. Bridge; river - For each bridge that you completely cross, fill in one segment in the bridges crossed scale bar and score the value indicated below the last segment filled.

3. Landmark - For each landmark that you visit, fill in one segment in the landmarks visited scale bar and score the value indicated below the last segment filled. To visit a landmark, you must pass by the letter than identifies it, not the associated building next to it. There are a total of eleven landmarks on the map; visit nine or more to earn 45 points.

   Our player crossed six of the seven bridges and visited seven of the eleven landmarks, scoring 36 and 28 points respectively. Think of the landmark identifiers as the plaques or signs that tell you what you are standing in front of!

4. Building - Color in all the buildings that you saw, scoring one point for each (regardless of its size or shape). To see a building, simply draw a line in front of any part of it. Do not color in or score points for landmarks.

5. Trees - Color in all the trees that you passed in front of and score one point for each. To score nine points for the trees 'hidden' inside of landmark H, you must draw a closed loop on the streets surrounding it. Otherwise, you do not score points for these trees.

   Our player passed by 51 buildings and 32 trees. They were not quite able to draw a closed loop around landmark H to score nine more points for the trees inside it. This example also demonstrates how to score trees when your line ends halfway through that map square.

6. Map squares - Find all the places where you drew lines to the edge of the map, and sum the value of the coordinates written beside them.

7. Drafting - Sum the value of all the bonuses that you used (filled triangles) in both the IMMEDIATE USE and RESERVED USE columns. Do not score points for any reserved bonuses that you did not use.

   Our player scored 26 points by extending several lines to the edge of the map, and 17 points for using various drafting bonuses. In our example, the footpath bonus was reserved but not used, so no points were scored for it.

Total Score

For each of the seven bridges that you crossed, you earn the points from one item in the map legend. For example, if you crossed five bridges, you score the five highest values and ignore the two lowest.

Our player was able to cross six of the seven bridges on the map. Excluding their lowest scoring legend item, their total score was a very respectable 209 points!

In the case of a tie, the winner is the player who crossed the most bridges. If still tied, the winner is the player who saw the most landmarks. If still tied, the winner is the player with the highest score in one legend item.

The winner is the player who scores the most points! Will it be the person who crossed the most bridges, or a player who focused on maximizing points in specific categories? With more than 100 places to start exploring Königsberg, each game is different so you'll only find out by playing!

Variant: Committed Scoring

Experienced players wanting an additional challenge can use the following rule: when you cross a bridge, you must immediately select one item from the map legend to score at the end of the game. If you cross four bridges, you will score the four items that you selected as the game progressed, which may or may not end up being your best ones!

Now, Where Were We?

The turn tracker can also be used as a 'save point' to continue the game at a later time! If you must interrupt play for some reason, simply note the player turn order and who should roll first when the game resumes.

Left image, the turn tracker prepared for a four-player game. Right image, the tracker at the end of the third player's turn in round three. If the game was paused at this point, it would resume with the fourth player's turn.

Rules for Solo Play

The solo player version of Seven Bridges is an entertaining challenge that is often won or lost on the last turn! The rules are exactly the same as a two-player game, except now you will be competing against an AI opponent named Euler, and he will score points for all the parts of Königsberg that you do not visit!

Euler is the second player, so he rolls the dice first in rounds two and four.

Drafting

As in a two-player game, both you and Euler will draft three dice per turn. Euler will always draft the lowest value die as indicated by the numbers next to the IMMEDIATE USE column, and chooses 3 dice over 2 dice. Simply discard the dice that Euler drafts; you won't be mapping his progress.

To make your task more difficult, Euler always drafts a die with a 3 face on it when given the opportunity. For example, if Euler will draft a + and there are two or more to choose from, he will take one with a 3 face before taking one with a 2 face. This will prevent you from getting as many 3 dice if you re-roll the dice later in the turn!

Scoring

At the end of five rounds, calculate your total score exactly as you would in a multiplayer game. Then calculate Euler's score:

1. Street; footpath – Euler scores 0 points; he doesn't make any closed loops.
2. Bridge; river – Euler crosses all the bridges that you did not cross. Determine his score using the bridges crossed scale bar: if he had to cross two of the seven bridges, he would score 4 points.
3. Landmark – Euler visits all the landmarks that you did not visit. Determine his score using the landmarks visited scale bar: if he had to visit four of the eleven landmarks, he would score 10 points.
4. Building – Euler passes by all the buildings that you did not. There are exactly 100 buildings on the map: if you passed by 55 buildings, Euler would score 45 points.
5. Trees – Euler passes by all of the trees that you did not. There are exactly 100 trees on the map as well: if you only saw 30 trees, Euler would score 70 points.
6. Map squares – Euler visits all the edges of the map that you did not. There are 80 points available: if you scored 35, Euler would score 45 points.
7. Drafting – Euler uses all the drafting bonuses that you did not use. There are 40 points available: if you scored 20 points, Euler would also score 20 points.

Euler's total score is the sum of items two thru seven, regardless of how many bridges you crossed.

If our player had been competing against Euler in a solo game, they would have eked out a win by just four points, 209 to 205! Euler scored 1, 10, 49, 68, 54 and 23 points in his legend items. Since Euler always drafts the lowest value die, there are a few ways to 'manipulate' him to your advantage!

Solo Difficulty

There are nine difficulty levels in solo play, depending on where you start the game. Some starting squares are easy (Levels 1-3) because they are next to bridges and landmarks; other starting squares (Levels 7-9) make it extremely difficult to score enough points to beat Euler!

Leonhard Euler (1707 – 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics. Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time. The mathematical constant e (≈2.71828) is named in his honor.

In 1735 Euler presented a solution to the problem known as the Seven Bridges of Königsberg: whether it was possible to follow a path that crossed each bridge exactly once before returning to the starting point. It's not possible – feel free to try it on our map! – and his solution is considered to be the first theorem of graph theory (Wikipedia).

About the Map

The game's map was inspired by the beautiful, highly-detailed map of Königsberg produced by renowned German cartographer Johann Homann (1664 – 1724) for his Grand Atlas of all the World, which shows the city as it was when Euler resolved the Seven Bridges problem.

The bridges and landmarks identified on the game's map are:

#	Bridge	Letter	Landmark
1	Green Bridge	A	Altstadt Monastery
2	Offal Bridge	B	Lastadie District
3	Honey Bridge	C	Altstadt Church
4	New (High) Bridge	D	Löbenicht Town Hall
5	Grocers Bridge	E	Kneiphof Town Hall
6	Smith's Bridge	F	Königsberg Cathedral
7	Wooden Bridge	G	Lomse District
		H	Kneiphof Suburbs
		I	Kneiphof Monastery
		J	Kneiphof Hospice Church
		K	Alte Garten District

In the year 1724, King Frederick William I of Prussia amalgamated the three towns of Altstadt, Löbenicht, and Kneiphof into the city of Königsberg.