Worksheet 6.0 (page 1 of 2)
Bulls and cows
This is a version of a game called Mastermind. This version uses digits instead of
colours.
Two-digit version
The simplest version uses only two digits. Make up a two-digit number from 10 to
98 with no repeats (for example, not 11 or 22 and so on). Keep it hidden. Both
players try to figure out the other’s hidden number. This is done by guessing and
receiving clues in the following way.
 If a digit is right, and is in the right place it is a ‘bulls-eye’, or a Bull.
 If a digit is right, but is in the wrong place it is a Cow.
 If a digit is not in the number, it scores nothing.
After your guess your opponent must tell you, truthfully, how many bulls and how
many cows you have scored. Write your guess and its score in a table.
Players take turns to guess each other’s numbers. The first to figure it out
correctly wins.
A typical game follows.
The hidden number is 35.
Guess
Bulls
Cows
12
0
0 (a ‘no score’ is useful information)
34
1
0 (either 3x or x4)
56
0
1 (either x5 or 6x; so it is either 64 or 35)
64
0
0 (try one possibility – missed this time)
35
2
0 (Got it!)
Three-digit version
This is more complex and will take more turns for someone to win, unless a
player guesses correctly. Good players can usually get there in 6 or 7 turns.
Keep a list of digits so you can cross them off as you eliminate them.
Four-digit version
This is much more complex, but good players can get there in about 10 turns.
CSF Sample Units: Years 8 to 10 Maths – Strategy games
Worksheet 6.0 (page 2 of 2)
Use the spreadsheet
In the spreadsheet ‘Bulls&Cows’ the computer hides a number and will tell you
how many Bulls and Cows you score each time. Use the spreadsheet to improve
your skills at the 2-, 3- and 4-digit games.
CSF Sample Units: Years 8 to 10 Maths – Strategy games