```FLORIDA HIGH SCHOOLS COMPUTING COMPETITION '82

1.1  Write a program to play the following game:  The computer
picks a number to print the message "I am thinking of a number.
What is the number?"  The computer tells the user if the guess is
too high or too low.  Use numbers between 1 and 100 and allow the
user 7 guesses.

1.2  Write a program to find all numbers less than 50 which can be
written as the sum of two squares, i.e. 20 = 2^2 + 4^2.

1.3  Write a program to determine the sum of all numbers between
100 and 1000 divisible by 14.

1.4  Write a program that will generate a random time (1-12, 0-60)
for hours, minutes.  Add to this another random time.  Have the
computer print both times using (:) to separate hours from minutes
and the time that the clock would read when added together.  (Use
only a 12-hour clock).

1.5  Write a program to calculate the roots of a quadratic
equation.  The equation must be in the following form:
ax^2 + bx + c = 0.
___________
roots = -b +- \/  b^2 - 4ac
-------------------
2a

Have the computer print roots if the roots are real.  Print only
"complex" if not real.  The user inputs the coefficients a, b, c.

1.6  Write a program that lists the prime factors of a positive
integer <= 100.

1.7  Write a program that calculates the future value of an
investment (T) when interest is a factor, using the following
formula:
N*y
T = P(1 + i/N)

where T = total value after Years (Future value)
P = initial investment
i = nominal interest rate
N = number of compounding periods per year
y = number of years

1.8  Write a program to find three positive integers such that
their sum is 43 and the sum of their cubes is 17299.

1.9  Write a program that prints any keyboard symbol on the screen
for exactly 45 seconds.

1.10  Write a program to accept a user's terminating decimal input
and print its equivalent fractional notation.

1.11  Write a program that prints an asterisk in the center of the
screen.  When the user types a U the star moves up, D down, R to
the right, L to the left.  Do not leave a sketched path, only one
asterisk appears on the screen.

2.1  Write a program that calculates the day to the week that a
given date falls upon for 1982.  January 1 was a Friday.  Let the
user enter the date in numeric form in the order of the month and
day.  May 29 will be entered as 5, 29.

2.2  Write a program that calculates the area of a polygon, using
the following formula:

Area = [(X1 + X2) * (Y1 + Y2) + (X2 + X3) * (Y2 + Y3) +
.... (Xn + X1) * (Yn + Y1)] * 1/2

where n = the number of vertices.  Let the user supply the x and y
coordinates of all vertices.  Have the computer ask for the number
of vertices.

2.3  Write a program to find a five digit number which when
multiplied by four has its digits reversed.

2.4  153 is an interesting number because 153 = 1^3 + 5^3 + 3^3.
Write a program to find three other three-digit numbers like 153.

2.5  Write a program to make a computer print the user's name in a
zigzag pattern from one side of the screen to the other and back
again (only one letter per line.)

2.6  Write a program to repeatedly print a stick figure.  Make the
figure wave his arm.

2.7  Write a program that will accept the user's letters.  Have
the program randomly scramble them until a word appears.  (The
user's letters will be able to make a word).

2.8  Write a program to drill typing skills.  Have the computer
print four random letters, numbers, or symbols.  The computer is
to wait for the user's response.  If the user types all four
correctly, print time that elapsed.  If wrong, tell which keys
were not typed correctly.

2.9  Write a program that asks the user for the price of an item
and what denomination of money the user has.  Have the computer
print the change returned using the fewest coins and bills
possible.  (No half-dollars to be used).

2.10  Write a program that converts a measure given in anglo units
to metric units.  Make the following conversions available:
inches to centimeters, feet to centimeters, feet to meters, yards
to meters, miles to kilometers.

Note: 1 inch =      2.54 centimeters
1 foot =        12 inches
1 yard =         3 feet
1 meter =      100 centimeters
1 kilometer = 1000 meters
1 mile =      5280 feet

2.11  Write a program to find four integers A, B, C and D which
satisfy

A^B x C^D = ABCD

2.12  Write a program that calculates the number of days between
two given dates in the same year.  The program should assume there
is one day between today and tomorrow, there are two days between
May 1 and May 3.

2.13  Write a program to print a check.  Let the user provide the
date (using numbers for month, day and year), amount, and payee of
the check.  The program is to translate the date and amount to
words and prints providing spacing within the check.

3.1  Write a program to play Mastermind where the user guesses the
computers arrangement of six colors (red, white, blue, green,
yellow, black).

3.2  Write a program to plot points on a set of coordinate axes.
The user provides the x and y coordinates of all points to be
plotted, the end points of the x- and y-axis, and the increment
between points on each axis.

The axis are to be switched so that the x-axis runs horizontal.
The axes do not necessarily intersect at zero.  Where the axes
meet is to be printed at the top of each graph.

INTERSECTION AT (50,50)

* * * * * * * * * * * * * * * * * * * *
*
*               + (52, 58)
*
*     +
*
*           +
*
*
*
*

3.3  A magic square is an array of numbers with just as many rows
as columns whereby the sum of any row, column or diagonal is
always the same.  No number may be used twice in constructing the
array.

Write a program to generate magic squares up to 12 x 12.  Let the
user specify the size desired.  The sum in question may be
anything.

3.4  Write a program to add and multiply any two Roman numerals
inputted.  Perform both operations on the numbers and print both
answers in Roman form.  Have the computer type out the Arabic
equivalent underneath each set of equations.

3.5  A 4 digit squumber is a number in which if you add the two
left digits to the two right digits you get a number which when
squared brings you back to the original number.

example:  2025
20 + 25 = 45 and (45)^2 = 2025

Write a program to find all 4 digit squumbers!

3.6  Write a program to play NIM with a user.

3.7  Write a program that accepts a list of 16 numbers from the
user.  Have the computer ask the user for another number.  Have
the computer print between which two numbers in the list the last
number falls.

3.8  BONUS

Write a program that guesses the state of the United States of
America that the user has in mind.  The computer asks yes or no
questions.

3 points if guessed in 6 or less questions
2 points if guessed in 7-9 questions
1 point  if guessed in 10-12 questions

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