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08 Magic Numbers.TXT
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1997-05-25
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INSTRUCTIONS FOR
VIDEOCART-8
CARTRIDGE GAMES
Exclusively for use with the Fairchild Video Entertainment System.
=========
FAIRCHILD
=========
VIDEOCART is a trademark of Fairchild Camera and Instrument Corporation.
On Your Mark
Get set and go with these two thought provoking one-player games. Take your
Videocart cartridge and, with the front label facing out, and the top label
facing up, insert it gently in the chute makred 'insert cartridge.' To
remove the cartridge, press the 'press to eject' bar, then slide the
cartridge out.
1. Mind Reader
Can you read the computer's mind? Use logic to guess the random number the
computer is thinking of and you become a Mind Reader. The computer will
give you clues, but if you don't use logic, some of the clues might throw
you off the track!
Mind Reader is a one-player game, you against the computer. The object is
to guess the number the computer is thinking of. The number can be 2 to 5
digits long (see options). You have 20 guesses or a time limit (see
options).
SETTING UP THE GAME. Press RESET, then button 1. An S? will appear asking
you if you are ready to start. Press START for a 3-digit, 20 guess game
(see options).
OPTIONS. Number of Digits. You can play Mind Reader with two to five digit
numbers, the larger the number, the harder the game.
Press RESET, then button 1 to get Mind Reader on the screen. When the S?
appears, press button 2 (MODE), then button:
1 for 2-digit numbers.
2 for 3-digit numbers.
3 for 4-digit numbers.
4 for 5-digit numbers.
When S? appears again, press START to start the game.
Time. You have a choice of figuring out the computer's number in 20 guesses
or a specific time limit.
Playing with 20 guesses is automatic. If you want to play a game using a
time limit instead, when the S? appears, press button 1 (TIME), then button:
1 for 2 minutes.
2 for 5 minutes.
3 for 10 minutes.
4 for 20 minutes.
When the S? appears again, press START to start the game. The number will
come up and the clock will start counting down. You cannot stop the clock
during a game of Mind Reader. To do so would give you an advantage over
the computer. You can think while the clock is stopped, the computer can
not!
Note: The MODE and TIME options can be set in either order.
PLAYING THE GAME. Let's assume that a 3-digit, 20 guess game is on the
screen. (Press RESET, then buttons 1 and 4).
How the Hand Controllers Work. The number (000) at the left side of the
screen just above the dark score line is the QUESTION LINE (see Screen
Layout). This is the number you are working with.
Pushing Left or Right will move the CURSOR (little line) under the digits
to the right or left from digit to digit. This tells you which digit you
are working with.
Twisting Left -- Cycles the digit that the cursor is under DOWN from 0 to
1 (0, 9, 8, ...2, 1).
Twisting Right -- Cycles the digit that the cursor is under UP from 0 to 9
(0, 1, 2, ...8, 9).
Pushing Down -- Enters a guess. The computer will respond with clues to that
guess. After a round is over, pushing down clears the screen and sets up a
new round with the same variables.
Screen Layout. After a game gets going, you will see that there are three
rows of numbers on the screen.
The bottom line is the ANSWER LINE. This is the line where the computer
gives back its clues to the number on the question line. When you push down
and enter a guess, the number on the question line jumps up to the answer
line and appears there along with the computer's clues for that number.
The top line is the PREVIOUS ANSWER line. Each time a guess is entered and
the question line number jumps to the answer line, the number that was on
the answer line jumps to the previous answer line to give you a comparison
between the guess and the previous guess.
323 TT <------- Previous Answer
233 HT <------- Answer
233 <------- Question
-----------------
Computer's Score ----> 15 12 23 <------- Your Score
^
|
Number of Guesses Left --------
(or Time)
Each time a guess is entered by pushing down on the hand controller, the
numbers on the screen 'roll up,' that is, move up from one line to another.
Any information contained in the previous answer line is lost the next time
a guess is entered.
Clues. The computer gives one clue for each digit on the answer line. The
clues are:
H -- "HIT" means that one digit in your guess (the question line) is the
same as one digit in the computer's mystery numbver and it IS in the
correct position.
T -- "TRANSPOSE" means that one digit in your guess (the question line) is
the same as one digit in the computer's mystery number but it is NOT
in the correct position.
_ -- Blank (no symbol) means that one digit in your guess is not at all like
any digit in the computer's mystery number.
Remember: The computer compares its number against yours DIGIT FOR DIGIT, and
gives you clues that way. If two digits in your guess are the same, and only
one of those digits is in the computer's mystery number, it will give you
clues for BOTH of your digits, even though it is only using one of them.
Beware! Some of the clues you get may lead you astray!
SCORING: 20 Guess Games. You have 20 guesses in which to find the mystery
number. The computer gets one point for each guess you use. You get one
point for each guess you have left, plus 5 bonus points, if you guess the
mystery number before your 20 guesses are used up.
Time Limit Games. The score svary depending on the number of digits you have
in the mystery number.
2-digit mystery number scores 2 points per digit.
3-digit mystery number scores 3 points per digit.
4-digit mystery number scores 4 points per digit.
5-digit mystery number scores 5 points per digit.
If you won a 4-digit game, you would get 16 points, etc. The first one (you
or the computer) to get to 100 wins the game. When either player gets to
100, the screen will clear and a G? will appear asking if you want to play
another game.
A Few Practice Rounds. Let's play a few practice games to get used to what
the computer is telling us with its clues.
The following games are one person's method of playing Mind Reader and are
meant only to be informative. There are many strategies to playing Mind
Reader and no doubt you will find one that is best for you.
Assume that we have set up a 3-digit, 20 guess game.
990
990
------------------
01 19 00
Our first guess on the question line is 990. The computer's response on the
answer line 'blank,' 'blank,' 'blank,' meaning that there are NO 9's or 0's
in its mystery number.
990
778 HT
778
------------------
02 28 00
Our second guess on the question line is 778. The computer's response is
HT_. (HIT, TRANSPOSE, BLANK). That means that one of our numbers is right
and in the correct position, and one more is right but not in the correct
position.
Since the computer gives us one clue for each digit and we have two symbols
and a blank, we can associate the blank with the 8 and the two symbols with
the 7's. Now we know that there are no 8's and at least one 7. Why AT LEAST
ONE 7 and not FOR SURE TWO 7's? Remember that the computer looks DIGIT BY
DIGIT at our guess when comparing it to its mystery number. One of the 7's
could be giving us the HIT because we have a 7 in the same position as the
computer, and the other 7 could be giving us a TRANSPOSE because the computer
has a 7 in its number and so do we, even though it is the same 7!
778 HT
765 HH
765
------------------
03 17 00
Assuming that there is only one 7 in the computer's number, our third guess
is 765. (We are assuming the first 7 is correct). The computer's response is
HH. This tells us that not only was our assumption about the first 7
correct, but that there is a 6 or a 5 in the mystery number too, but not
both.
765 HH
764 H
764
------------------
04 26 00
Our next guess is 764. (We are assuming that the 6 is correct). The
computer's response is H. We lost a HIT. Our assumption that the 6 was
correct is wrong. Looking at the previous answer line and the answer line,
the only difference is that the 5 changed to a 4 and we lost a HIT. This
can only mean that the 5 was correct and that there are no 4's or 6's. Let's
try 3's.
764 H
735 HH
735
------------------
05 15 00
Our next guess is 735. The computer's response is HH. This means that the
7 and the 5 are correct and there are no 3's. Let's try 2's.
764 H
735 HH
725WIN725
------------------
05 15 20
We've guessed the mystery number! Let's try one more game. Push down the
hand controller for a new game.
990
990
------------------
06 19 20
Our first guess is for 9's and 0's. The computer's response is blank. There
are no 9's or 0's.
990
887 T
887
------------------
07 18 20
Our second guess is for 8's and 7's. The computer's response is T. Since
there is only one symbol, it must be associated with the 7. This means that
there is a 7 in the mystery number, but not in the last position.
887
576 H
575
------------------
08 17 20
Our next guess is 576. This trys the 7 in the middle position and also asks
about 5's and 6's. The computer's response is H. We have hit the 7 and
there are no 5's or 6's.
576 H
473 HTT
473
------------------
09 16 20
Let's try 4's and 3's. The computer's response is HTT. We know the HIT is
for the 7, so there must be a 4 and a 3 in the mystery number, only
transposed! Let's turn ours around.
576 H
473 HTT
374WIN374
------------------
09 16 41
Again, we have guessed the mystery number! There are literally hundreds of
ways to get the most information out of one guess. The games illustrated
here are only one example. Play around and you will find the method that
works best for you.
2. Nim
Catch the computer in a binary bind, and you win every time! Nim is the
oldest two-person mathematical game known to man. Nim is believed to be
Chinese in origin. The basis of the game is simple. There are several
piles of objects. Each pile contains from 1 to 15 objects. Each player
takes turn taking any number of objects out of any pile. You have to take
at least one object, and you can take objects out of only one pile. The
player who takes the last object off the table wins.
In the 21st century version of Nim, you play against the computer. You have
a choice of 3, 6, or 9 piles. The objects in the piles are numbers, 1 to
15. The player who takes the last number off the screen wins.
Setting Up The Game. Press RESET then button 2. An S? will appear asking
you if you are ready to start. Press START for a 3-pile, no time limit game.
OPTIONS: Number of Piles. You have a choice of 3, 6, or 9 piles to play
with. The more piles, the harder the game.
Press RESET, then button 2 to get Nim on the screen. When the S? appears,
press button 2 (MODE), then button:
1 or 2 for 3 piles.
3 for 6 piles.
4 for 9 piles.
When the S? appears again, press START to start the game.
Time. You have a choice of playing with or without time limit. Playing
without a time limit is automatic. To play a game with a time limit, when
the S? appears, press button 1 (TIME), then button:
1 for 2 minutes.
2 for 5 minutes.
3 for 10 minutes.
4 for 20 minutes.
When the S? appears again, press START to start the game. The game will
come up and the clock will start counting down. You cannot stop the clock
during a game of Nim. To do so would give you an advantage over the
computer. You can think while the clock is stopped, the computer can not!
Note: The MODE and TIME options can be set in either order.
PLAYING THE GAME. Let's assume a 3-pile, no time limit game is on the
screen. (Press RESET, then buttons 2 and 4).
How the Hand Controllers Work. There are three squares on the screen. These
are piles. Each square contains a number. This is the number of objects in
that pile.
The pile with the small square under it is the pile that you are working
with (this square is red on color TVs and light grey on black & white TVs).
This is the pile you have chosen to take objects out of.
Pushing Left or Right -- moves the small indicator dot (called a 'cursor')
right or left from square to square. This lets you choose which pile you
want to take objects out of.
Pushing Forward or Back (for 6 or 9 pile games only) -- this moves the
cursor up or down from square to square. In a 6 or 9 pile game, you can
move from square to square by going right, left, up or down.
Twisting Left -- decreases the number of objects in the pile. Decreasing a
square from 12 to 7 means that you have taken 5 objects out of that pile.
Twisting Right -- increases the number of objects in the pile. This is in
the case you have taken too many. You cannot increase the number in a
square past what was previously there.
Pushing Down -- tells the computer that you are satisfied with the number of
objects you have taken. You cannot skip a turn.
At the end of a game, PUSHING DOWN clears the screen and sets up a new game
with the same variables.
After you have taken a number of objects out of a pile, it is the computer's
turn. It will move the cursor to the square of its choice and remove some
of the objects. After that, it is back to you!
SCORING. Scoring depends on the number of piles in the game and whether or
not there is a time limit.
The number in the lower left corner of the screen is the computer's score.
The number in the lower right corner is your score.
No Time Limit
3 pile games score 2 points.
6 pile games score 5 points.
9 pile games score 8 points.
Time Limit
2-minute games
3 piles scores 10 points.
6 piles scores 17 points.
9 piles scores 25 points.
5-minute games
3 piles scores 8 points.
6 piles scores 14 points.
9 piles scores 20 points.
10 or 20-minute games
3 piles scores 4 points.
6 piles scores 7 points.
9 piles scores 10 points.
In summary, the less time and more piles, the higher the score. The first
player to reach 100 (you or the computer) wins the game. When either
player reaches 100, the screen will clear and a G? will appear asking if
you want to play another game.
STRATEGY. There is no "winning strategy" in Nim. People have been thinking
up ways to beat this game for centuries and will probably continue to do so
for centuries to come. The best "winning strategy" is to find one that works
for you!
One method you can use to beat this 21st century version of an old game is to
think the way the computer does -- in BINARY.
Binary numbers use only two digits to make up the number -- 0 and 1. The
binary numbers from 0 to 15 (the limits to this game of Nim) are all 4 digits
long -- 0000 to 1111.
It helps if you think of the digits of a binary number as placeholders, that
is, they stand for something else. The placeholders in the binary digits
0000 to 1111 stand for 8, 4, 2, and 1. Lets see some examples
PLACEHOLDERS
8 4 2 1
Binary number: 1 0 1 0 stands for: 8+0+2+0 = 10!
Let's try it again.
PLACEHOLDERS
8 4 2 1
0 1 1 0 stands for 0+4+2+0 = 6,
1 1 0 0 stands for 8+4+0+0 = 12,
0 0 1 0 stands for 0+0+2+0 = 2,
1 1 1 1 stands for 8+4+2+1 = 15!
Got it? Each '1' means the placeholder counts, each '0' means that it does
not. Just add 'em up!
Now, let's apply the Binary Strategy to a game of Nim. Let's assume that a
3-pile, no time limit game is on the screen. The three piles that come up
are:
---- ---- ----
|13| |14| | 1|
---- ---- ----
*
Translated to binary, that is
8 4 2 1
1 1 0 1 = 8+4+0+1 = 13
1 1 1 0 = 8+4+2+0 = 14
0 0 0 1 = 0+0+1 = 1
The trick to this strategy is to make sure you move to a 'safe' position. To
do this, add up the COLUMNS -- the '8' column, the '4' column, the '2'
column, and the '1' column. If the total of the column is 0 or an even
number, you are in a 'safe' position. If it is an odd number, you are not
in a 'safe' position, and need to change the binary number so you will be in
a 'safe' position.
Let's add up our columns to see if we are in a 'safe' position.
8 4 2 1
1 1 0 1 = 13
1 1 1 0 = 14
0 0 0 1 = 1
-------
column totals: 2 2 1 2
We would seem to be 'safe' everywhere except in the '2' column. What can we
do to make that column 'safe'? It seems teh best way would be to get rid of
the '1' in the '2' column, bringing the column total to zero -- a 'safe'
position. Removing the '1' means we are taking 2 away from the second
number -- 14, in other words, reducing 14 to 12.
This is our move:
---- ---- ----
|13| |12| | 1|
---- ---- ----
*
8 4 2 1
1 1 0 1 = 8+4+0+1 = 13
1 1 0 0 = 8+4+0+0 = 12
0 0 0 1 = 0+0+1 = 1
-------
column totals: 2 2 0 2 - a 'safe' position.
The computer will try to make our position unsafe again. Its move:
---- ---- ----
|11| |12| | 1|
---- ---- ----
*
8 4 2 1
1 0 1 1 = 11
1 1 0 0 = 12
0 0 0 1 = 1
-------
column totals: 2 1 1 2 - an unsafe position!
We are unsafe in the '4' and '2' column. It doesn't look as if taking 4 or 2
away from a number will do any good. It would make one column safe, but not
both. Since we can only work with one pile at a time, the only way to make
both columns safe is to subtract 4 from the middle number and add 2 -- in
other words, remove a '1' from the '4' column and add a '1' to the '2' column.
This is the binary equivalent of subtraction. We have reduced the 12 to 10.
This is our move:
---- ---- ----
|11| |10| | 1|
---- ---- ----
*
8 4 2 1
1 0 1 1 = 11
1 0 1 0 = 10
0 0 0 1 = 1
-------
column totals: 2 0 2 2 - a 'safe' position.
The computer's out to make it unsafe for us. Its move:
---- ---- ----
| 0| |10| | 1|
---- ---- ----
*
8 4 2 1
0 0 0 0 = 0
1 0 1 0 = 10
0 0 0 1 = 1
-------
column totals: 1 0 1 1 - an unsafe position.
The computer has us unsafe in every column! The only way to get back to a
safe position is to change the middle number so there is a '1' in the '1'
column and get rid of the others. Our move:
---- ---- ----
| 0| | 1| | 1|
---- ---- ----
*
8 4 2 1
0 0 0 0 = 0
0 0 0 1 = 1
0 0 0 1 = 1
-------
column totals: 0 0 0 2 - a 'safe' position.
We have maneuvered the computer into taking the next to the last object -- we
have won! The only thing it can do is take one of the '1's. Its move:
---- ---- ----
| 0| | 1| | 0|
---- ---- ----
*
8 4 2 1
0 0 0 0 = 0
0 0 0 1 = 1
0 0 0 0 = 0
-------
column totals: 0 0 0 1
To make it safe, and win, remove the '1'. Our move:
---- ---- ----
| 0| | 0| | 0|
---- ---- ----
*
We have won the game.
Have Fun
If you have questions about this Videocart(TM)* cartridge or your Video
Entertainment System, call the toll free numbers in the back of your console
instruction booklet.
Other exciting Videocart cartridges are available from your Fairchild dealer
or, for more information, write:
Fairchild Consumer Products
4001 Miranda Avenue
Palo Alto, CA 94304
*VIDEOCART is a trademark of Fairchild Camera and Instrument Corporation
Copyright (C) 1977 Printed in U.S.A.