Number Bulls & Cows | Number games

One player tries to guess the other player's mathematical rule.

Description

The Chooser thinks of a rule that converts one number into another (a mathematician would call this a "function"). The Guesser then tries to guess the rule by testing it with different numbers.
For example, if the Chooser thought of the rule "double it and add one", the game might proceed as follows:
Guesser: "1" - Chooser: "3"
Guesser: "2" - Chooser: "5"
Guesser: "10" - Chooser: "21"
Guesser: "100" - Chooser" "201"
Guesser: "I think it's double and add one" - Chooser: "Correct!"
The rule can be anything you like, but sometimes the Guesser may have to guide the Chooser in the right direction; for example: "Try something larger", or "Try a negative number".

Examples

Here are some other suggested rules:

• The number of letters in the word for the number (6 -> 3).
• 100 minus the number squared (9 -> 19).
• The number reversed (17 -> 71)

Play Function Game

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Function Game | Number Games

One player tries to guess the other player's mathematical rule.

Description

The Chooser thinks of a rule that converts one number into another (a mathematician would call this a "function"). The Guesser then tries to guess the rule by testing it with different numbers.
For example, if the Chooser thought of the rule "double it and add one", the game might proceed as follows:
Guesser: "1" - Chooser: "3"
Guesser: "2" - Chooser: "5"
Guesser: "10" - Chooser: "21"
Guesser: "100" - Chooser" "201"
Guesser: "I think it's double and add one" - Chooser: "Correct!"
The rule can be anything you like, but sometimes the Guesser may have to guide the Chooser in the right direction; for example: "Try something larger", or "Try a negative number".

Examples

Here are some other suggested rules:

• The number of letters in the word for the number (6 -> 3).
• 100 minus the number squared (9 -> 19).
• The number reversed (17 -> 71)

Play Function Game

Visit our dedicated Function Game site:

www.functiongame.com

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Sprouts | Topological Games

The players take turns in joining dots according to simple rules, until one player cannot make a move.

Description

Start by drawing two or more spots on a piece of paper.
Players then take turns to make a move, according to the following rules:

• Draw a curve joining two spots, or a single spot to itself. The curve must not pass through another spot.
• Draw a spot on the new curve.
• No more than three lines can emerge from any spot.

The last player to be able to move wins.
The game is remarkably complicated, and even starting with two spots leads to an interesting game.

Example

In the following sample game with two spots Blue has the first move, and Red wins after 4 moves because Blue has no move:

History

Sprouts was invented by the mathematicians M. S. Paterson and J. H. Conway, and was analysed in Winning Ways, Academic Press, 1982.

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Gale | Topological Games

Players take turns in linking dots on overlapping grids. The first player to draw a continuous chain linking their ends of the board wins.

Description

To create the board first draw a rectangular array of 4 x 5 blue dots. Then draw an overlapping array of 5 x 4 red dots:


The players take turns in linking two adjacent dots of their own colour. No two links may cross. The first player to form a chain of links across the board, from top to bottom (blue) or left to right (red), wins.
The game can be played with larger overlapping arrays of n x n+1 dots. The game cannot be a draw because, to block their opponent, a player must themselves form a continuous chain.

Example

For example, in the following game blue wins by forming a chain from top to bottom:

 

History

Gale, also known as Bridgit, was invented by the mathematician David Gale.
It was described in "The Second Scientific American Book Of Mathematical Puzzles and Diversions", Martin Gardner, The University of Chicago Press, 1961.

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Cram | Topological Games

The players take turns linking pairs of dots on a grid. The first player unable to move loses.

History

The game was originally proposed by Geoffrey Mott-Smith who called it Plugg, and was described by Martin Gardner as the game Cram in "Mathematical Games: Cram, Crosscram and Quadraphage: New Games having Elusive Winning Strategies." Scientific American 230, 106-108, Feb. 1974.
It is related to the game Domineering, which is identical except that one player can only make vertical moves and the other player can only make horizontal moves.

Description

The game is played on a matrix of dots.
The players take turns in linking a pair of adjacent dots with a horizontal or vertical link. No dot can be linked more than once.
In the normal game the first player unable to move loses.
Alternatively, in the misère version, the first player who cannot move wins.

Strategy

Normal Cram has a simple winning strategy on boards with an even side. On an even-by-even grid the second player can win by making a symmetric copy of each of the first player's moves. On an even-by-odd grid the first player can win by making the first move on the centre two squares, and thereafter making a symmetric copy of each of the second player's moves.

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Domineering | Topological Games

The players take turns linking pairs of dots on a grid. The first player unable to move loses.

History

The game was originally proposed by Göran Andersson, and was described by Martin Gardner as the game Crosscram in "Mathematical Games: Cram, Crosscram and Quadraphage: New Games having Elusive Winning Strategies." Scientific American 230, 106-108, Feb. 1974. It can also be played using dominoes to cover up squares on a checkerboard, hence the name Domineering by which it is now more generally known.
It is related to the less-interesting game Cram, in which each player can make either vertical or horizontal moves.
It was described and analysed in the book "On Numbers and Games" by John Horton Conway, Academic Press, 1976.

Description

The game is played on a matrix of dots.
The players take turns in linking a pair of adjacent dots. The first player, Blue, always makes a vertical link, and the other player, Red, always makes a horizontal link. No dot can be linked more than once.
The first player unable to move loses.

Example

In the following game Red is unable to move, and so loses:

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Strategy Bulls and Cows | Word Games

Strategy

A simple strategy is to make each guess consistent with the answers you've been given so far. Thus your guess will either be the correct word, or one of the possible candidates for the correct word, and each guess will bring you closer to the correct word.
This is usually a pretty good strategy, but it can be very inefficient if you get a large number of hits early in the game. For example, suppose the guesses and answers have been:

• Guess: "WORK" - Answer: 0 Bulls, 0 Cows
• Guess: "WELL" - Answer: 3 Bulls, 0 Cows

From this we can deduce that the word must end in "ell", and so can be one of these eight candidates:
BELL, CELL, DELL, FELL, HELL, SELL, TELL, or YELL.
Using the simple strategy we might guess "BELL", but it could take up to six more guesses to get the word. We have seven chances in eight that we'll be left with seven candidates, making:
7/8 * 7 = 49/8 = 6.125 candidates remaining (on average).
A better strategy is to try and eliminate as many candidates as possible with a guess such as "CYST". Although this can't be the correct answer, it divides the candidates with the following possible answers:

• 0 Bulls, 0 Cows - Candidates left: BELL, DELL, FELL, HELL
• 0 Bulls, 1 Cow - Candidates left: SELL, YELL, TELL
• 1 Bull, 0 Cows - Candidates left: CELL

So there are four chances in eight that you'll be left with four candidates, three chances in eight you'll be left with three candidates, and one chance in eight you'll be left with one candidate, making:
(4/8 * 4) + (3/8 * 3) + (1/8 * 1) = 26/8 = 3.25 candidates remaining (on average).
This shows that "CYST" is nearly twice as good as "BELL" for the next guess.
When playing Word Bulls & Cows you can eliminate letters as efficiently as possible by guessing a series of words with no letters in common. My favourite set of words for four-letter Bulls & Cows is:
MYTH, DUCK, VERB, GASP, JINX, and WOLF.
which use 24 of the 26 letters. The best I've come up with for five-letter Bulls & Cows is:
BLACK, FIGHT, JUMPY, DROWN, and VEXES
which use 24 of the 26 letters with one letter repeated. If anyone can find five five-letter words with no letters in common I'd be interested to know.

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Word Bulls & Cows | Word Games

Players take turns in trying to guess each other's word.

Description

One player, the Chooser, thinks of a four-letter word and the other player, the Guesser, tries to guess it.
At each turn the Guesser tries a four-letter word, and the Chooser says how close it is to the answer by giving:

• The number of Bulls - letters correct in the right position.
• The number of Cows - letters correct but in the wrong position.

The Guesser tries to guess the answer in the fewest number of turns.
If either word has repeated letters the rule is that each letter can only count towards the score once, and Bulls are counted before Cows.

Example

For example, if the Chooser has thought of the word LOVE the replies for some guesses are as follows:

• Guess: FISH - Reply: 0 Bulls, 0 Cows.
• Guess: VAIN - Reply: 0 Bulls, 1 Cow.
• Guess: LANE - Reply: 2 Bulls, 0 Cows.
• Guess: VILE - Reply: 1 Bull, 2 Cows.
• Guess: LOVE - Reply: 4 Bulls, 0 Cows!

Click here for STRATEGY for "Bulls & Cows"

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Word Ladder Race | Word Games

Each player chooses a word with the same number of letters. Both players then try to make a word ladder between the two words. The player with the shortest ladder wins.

Description

A word ladder is a sequence of words in which only one letter changes at each step.
One player chooses a starting word, and the other player then chooses an ending word of the same length. Both players then try to find a word ladder between the two chosen words. The player with shortest ladder wins. If neither player can find a ladder the game is a draw.

Example

For example, if one player chose WINE and the other player chose BEER a possible word ladder could be as follows:

Variations

To make the game more exciting impose a time limit of five minutes.
For a more complicated variation of the game try Scrambled Word Ladder Race.

History

Word Ladders were first popularised as Doublets by the mathematician Lewis Carroll, who wrote the popular children's books "Alice in Wonderland" and "Through the Looking-Glass". They feature in many books of word puzzles.

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Scrambled World Ladder Race | Word Games

Each player chooses a word with the same number of letters. Both players then try to make a scrambled word ladder between the two words. The player with the shortest ladder wins.

Description

A scrambled word ladder is a sequence of words linked by either of the following steps:

• Change one letter to make another word.
• Scramble the order of the letters to make another word.

One player chooses a starting word, and the other player then chooses an ending word of the same length. Both players then try to find a scrambled word ladder between the two chosen words. The player with shortest ladder wins. If neither player can find a ladder the game is a draw.

Example

For example, if one player chose WINE and the other player chose BEER a possible scrambled word ladder could be as follows:

Variations

To make the game more exciting impose a time limit of five minutes.
For a simpler variation of the game try Word Ladder Race.

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Countdown | Word Games

Players compete to find the longest word from a set of 9 letters.

History

Countdown is a popular game show on the Channel 4 TV network in the United Kingdom. Two contestants choose a series of consonants or vowels, and then have 30 seconds to find the best word.

Description

The players take turns in choosing letters until 9 letters have been named. They then try to construct a word using just those letters. The player who has found the longest word wins.

Example

For example, if the players chose the letters:
QWERTYUIO
the players might find QUERY and EQUITY, EQUITY being the winner.

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Word Square | Word Games

Players create word squares with the same letters, and the one who creates the square containing the most words wins.

Description

Each player draws a 4 x 4 grid which they keep concealed from the other player.
They then take turns in naming a letter. As each letter is named each player must write it immediately into one of the cells in their grid: Players can choose any letter they like, and letters can be repeated.
When the grid is full the players count up the number of words they have made reading across, down, or diagonally, and the one with the highest score (out of a possible 10) wins.
One interesting aspect of the game is that you can either choose letters that help you complete words, or you can try to thwart your opponent's words.

Example

The following square scores the player 6 points for the words:
CARD, TOSS, COAT, RIPS, DOTS, and CUPS:

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Consequences | Word Games

The players take turns in contributing sentences to a story. The final story is then read out, hopefully with hilarious results.

Description

Each player starts with a piece of paper. The players each write a phrase as the first step in a story, and then fold the paper to hide the phrase before passing it to the next player.
When the players have completed all eight steps, the pieces of paper are unfolded in turn, and the players read out the completed, hopefully funny, stories.
The steps are as follows, where the things in brackets should be replaced by the chosen words or phrase:

• (boy's name)
• met (girl's name)
• in/at/on (place)
• He said (what he said)
• She said (what she said)
• He did (what he did)
• She did (what she did)
• The consequence was (what happened)

Example

Here's an example of a possible story:
Prince William met Rihanna at the zoo. He said "Save the polar bears!". She said "Don't be so sexist". He slipped on a banana. She took flying lessons. The consequence was that they got arrested.

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Pictionary | Drawing Games

One player has to get the other players to guess a word by drawing a picture.

Description

The players should be in two teams. One team secretly thinks of a common phrase and whispers it to one member of the other team, chosen as the artist.
The artist then has to get the other members of their own team to guess the phrase by drawing a picture. They are not allowed to give clues by talking, or drawing letters or symbols.

Variations

One variation is for the artist to draw the picture with their eyes closed.
A commercial version of this game has been marketed in the UK.

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Heads Bodies and Legs | Drawing Games

Players take turns in drawing a head, a body, and a pair of legs, without letting the other player see them. The point of the game is the fun of seeing the resulting pictures.

Description

Each player starts with a small piece of paper - half of A4 or US Letter is about right.
Each player begins by drawing a head in the top third of the sheet, and then folds over the paper so just the neck is showing:


The players then exchange pieces of paper, taking care not to let the other player see their drawing.
Each player then draws a body in the centre third of the paper, joining the neck lines, and folds over the paper so just the legs are showing:


Again, the players exchange pieces of paper.
Finally, each player draws legs and feet, joining the leg lines, and folds the paper so nothing is visible.


Finally, after exchanging again, each player opens their piece of paper to reveal the whole drawing:

Variations

An amusing addition is to add an extra stage in which each player folds the page to leave a blank strip at the bottom of the paper.
After exchanging, each player writes a name for the drawing in the blank space.

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Noughts and Crosses | Territory Games

Players take turns in marking squares on a 3 x 3 grid. The first player to get three squares in a row wins.

Description

This game, also called Ticktacktoe in the USA, is probably the best known pencil and paper game.
The game is played on a 3 x 3 grid, typically created by drawing a # on a piece of paper. One player is 'O' and the other is 'X'. Players take turns in drawing their symbol in one of the positions on the grid. The first player to make a line of three of their symbol horizontally, vertically, or diagonally wins.
If both players play perfectly the outcome is always a draw, but with inexperienced players the game is just complex enough to make the game interesting.

Example

For example, the following game shows how the first player can force a win by starting in the centre square if the second player is foolish enough to reply on the edge:

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Dots and Boxes | Territory Games

Players take turns in drawing lines between dots on a grid. The player who completes the most boxes wins.

Description

The game is played starting with a rectangular array of dots.
The two players take turns to join two adjacent dots with a horizontal or vertical line. If a player completes the fourth side of a box they initial that box and must draw another line.
When all the boxes have been completed the winner is the player who has initialled the most boxes.
The game is more complex than it initially appears, and even on a 4x4 grid there is plenty of opportunity for skilful play.

Example

The following game on a 3x3 grid is won by Blue, who scores 3 against Red's one:

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3D Noughts and Crosses | Territory Games

Players take turns in marking squares on a 4 x 4 x 4 grid. The first player to get four squares in a row wins.

Description

To make the board draw four 4 x 4 grids stacked vertically, representing a 4 x 4 x 4 cube. It is easier to visualise the cube if you draw the grids in perspective.
The players take turns in drawing their symbol, O or X, in one of the cells. The first player to make a line of four cells in any direction wins. Winning lines can be horizontal, vertical, diagonal within one grid, vertical between grids, diagonal between grids, or diagonal in all three dimensions.

Example

In the following game O started, and won by making the line shown highlighted:

History

Commercial versions of the game have been sold consisting of four perspex boards stacked in a cube, with black and white counters or marbles for making moves.

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Battleships | Territory Games

Players take turns in trying to guess the locations of the other player's ships on a grid.

Description

Each player draws two 10 x 10 grids, labelled along the sides with letters and numbers. On the left-hand grid the player secretly draws rectangles representing their fleet of ships:

 

The fleet

Each player's fleet consists of the following ships:

• 1 x Aircraft carrier - 5 squares
• 1 x Battleship - 4 squares
• 1 x Cruiser - 3 squares
• 2 x Destroyers - 2 squares each
• 2 x Submarines - 1 square each

Each ship occupies a number of adjacent squares on the grid, horizontally or vertically.

Play

During play the players take turns is making a shot at the opponent, by calling out the coordinates of a square (eg D5). The opponent responds with "hit" if it hits a ship or "miss" if it misses. If the player has hit the last remaining square of a ship the opponent must announce the name of the ship; eg "You sank my battleship".
During play each player should record their opponent's shots on the left-hand grid, and their shots on the right-hand grid as "X" for a hit and "O" for a miss:



The first player to lose all their ships loses the game.

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Go Moku | Territory Games

Players take turns in marking squares on a grid. The first player to get five squares in a row wins.

Description

The game is played on a large piece of squared paper, at least 15 x 15. The players take turns in marking a square with their symbol (eg O and X). The first player to get five squares in a row, horizontally, vertically, or diagonally, wins.

Variations

The game can also be played with black and white counters on a large board, such as a Go board.
In the basic game the first player has an advantage, so a number of rules have been introduced to reduce this:

• Overlines rule: Only a row of exactly five squares wins; rows of six of more, called overlines, do not count.
• Three and Three rule: A move must not simultaneously create two open rows of three squares (rows not blocked at either end by an opponent's square).
• Four and Four rule: A move must not simultaneously create two rows of four squares, whether blocked or not.
• These restrictions are sometimes only applied to the first player.

History

The game has been known under a number of different names, including Five in a Row, Go Bang, and Pegit.
Go-Moku is from the Japanese "go moku narabe", meaning "five piece line-up". It was introduced into Britain in the 19th century as Go Bang, probably a corruption of Go Ban, the name of the table used for playing Go.

Example

The following example shows a typical game won by the first player

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