A long time ago (around 1974) when I was in high school, I learned a logic
game called Bagels. This is a simple game that can be played
with just pencil and paper or (for those with good memory) without
any props at all.
The game is deceptively simple. If you play well though,
it can be fairly deep.
Do you want to take the role of
choosing a number
or guessing my number?
Rules:
- There are two opponents. One picks a number, and the other one
attempts to guess the number. The person picking the number must
give accurate answers to the guesses.
- The person picking a number picks a three digit number.
In this version, there may be no leading zeros, and digits
may not be repeated.
- The person guessing the number gives three digit numbers.
- The person who picked the number answers:
- Fermi -- One of the digits in the guess matches
one of the digits in the answer, and it is in the right
position.
- Pico -- One of the digits in the guess matches
one of the digits in the answer, but the digit is not
in the right place.
- Bagels -- None of the digits in the guess match
any of the digits in the answer.
Multiple answers may come out of a single guess. For examples,
look at the table below:
| Picked Number | Guess | Answer |
|---|
| 123 | 456 | Bagels -- None of the digits match. |
| 123 | 345 | Pico -- The 3 matches, but is in the wrong place. |
| 123 | 543 | Fermi -- The 3 matches, and is in the right place. |
| 123 | 321 | Pico Pico Fermi -- The 3 and
1 match, but are in the wrong place, and the 2 matches
and is in the right place. |
- Players take turns holding each role.
The one who averages the fewest guesses is the better player.
History:
I learned this is a math class about 1974.
Diane Resek and Pete Rowe of the Lawrence Hall of Science and Math in Berkeley
implemented this games in BASIC in the early 1970's.
For an example, see:
atariarchives.org
or
archive.org (look for BAGLES).
Both Diane Resek and Pete Rowe worked at Lawrence Hall of Science at the time.
Pete Rowe was the head of the computer program there, and Diane Resek
taught math.
Resek taught Rowe the game, and he programmed it for LHS.
Resek learned the game from Bill Rupley (also a math teacher at the time),
in the mid 1960's
who learned it on the East Coast.
The board game
Mastermind
uses similar rules and was introduced in 1970.
The Wikipedia article mentions an older game called
Bulls and Cows
which may "date back a century or more".
Also, see Bullseyes and Close Calls
for variations on the normal rules.
A quick read of the rules show that this is the basically the
same game as Bagels.
There are computer programs implementing this called "moo" dating back to 1968.
This game also seems to be known as
Fiddle Faddle Flop.
The book named
Family Math
describes Bagels.
Donald Knuth wrote a paper
The Computer as Master Mind. J. Recreational
Mathematics, 9 (1976-77), 1-6.
describing an optional solution for Master Mind.
He refers to the "Bulls and Cows" game as a similar game with a computer
implementation in 1968.
Another paper by
Thomas M. Fiore, Alexander Lang, and Antonella Perucca titled
Tactile Tools for Teaching: An Implementation of Knuth's Algorithm
for Mastering Mastermind describes a circular slide rule for
implementing Knuth's algorithm.