1.1  Write a program to produce the following initials for NCNB 
National Bank: 

           NN    N  CCCCC  NN    N   BBBB 
           N N   N  C      N N   N   B   B 
           N  N  N  C      N  N  N   BBBBB 
           N   N N  C      N   N N   B   B 
           N    NN  CCCCC  N    NN   BBBB 

1.2  NCNB programmers in Tampa use an IBM 3090 model 400 mainframe 
computer that has an MVS/XA (Multiple Virtual Storage/ Extended 
Architecture) operating system.  The machine is partitioned into 
two logical processors:  SYSTEM 1 is used for testing and all 
day-time batch jobs;  SYSTEM 2 is used to support on-line programs 
and some night-time batch jobs.  Write a program to display the 
processor name given the system #.  Examples: 

     INPUT: Enter #: 1          INPUT: Enter #: 2 
    OUTPUT: SYSTEM 1           OUTPUT: SYSTEM 2 

1.3  With assets over 66 billion dollars in 1989, NCNB is the 
largest bank in the southeast United States.  Let's assume that 
the Tampa Application Systems Center staffs 66 programmers.  If 
there is a direct correlation between the number of programmers 
staffed in Tampa and the amount of money the bank has in assets, 
then display the total amount of assets NCNB will have if N more 
programmers are hired.  Example: 

     INPUT: Enter N: 4 

1.4  Write a program to help the post office determine the county 
in which a person lives, given his/her zip code.  Use the 
following as data: 

     HILLSBOROUGH - 33612  33613  33620  33510 
     PINELLAS -     33701  34685  34646 
     PASCO -        33525  34249  34690 


     INPUT: Enter zip code: 33525 

1.5  NCNB's dynamic chairman, Hugh McColl, resides at the national 
headquarters in Charlotte, North Carolina.  His secretary would 
like to issue a statement to all the employees concerning McColl's 
financial goals.  Write a program that accepts two numbers (MMM - 
amount in billions of dollars, and YYYY - year), and then produces 
a statement in the following form: 
     INPUT: Enter MMM: 100 
            Enter YYYY: 1995 
            THE YEAR 1995 
1.6  Vickie manages 7 people in the Trust Division at NCNB.  Her 
associates pay an average of 50,000 coupons monthly.  The work 
load is divided as evenly as possible among her associates so that 
no one person has more than one extra coupon to pay than another 
person.  Write a program to calculate the MAXIMUM number of 
coupons that any one of N associates must pay if C coupons come in 
for payments.  Examples: 
     INPUT: Enter N associates: 7 
            Enter C coupons: 49000 
    OUTPUT: 7000 
     INPUT: Enter N associates: 7 
            Enter C coupons: 49002 
    OUTPUT: 7001 
1.7  NCNB programmers code their programs primarily in COBOL: 
COmmon Business Oriented Language.  Each program is required to 
have these four divisions (in order): IDENTIFICATION, ENVIRONMENT, 
DATA, and PROCEDURE.  Write a program to display those divisions 
coming before and after a division given as input.  Multiple 
divisions on a line are to be displayed in order and with 2 spaces 
in between.  If none occur before/after entered division, then 
display NONE for that part.  Examples: 
     INPUT: Enter division: DATA 
            AFTER = PROCEDURE 
     INPUT: Enter division: IDENTIFICATION 

1.8  NCNB is the largest banking company in the South and the 7th 
largest in the nation.  NCNB has statewide banks in four states:  
Florida, North Carolina, South Carolina, and Texas.  It also has 
banks in Baltimore, Atlanta, and northern Virginia.  For 1990, 
NCNB will recognize the following number of holidays in each of 
the states:  10-FL, 8-NC, 7-SC, 10-TX, 11-MD, 10-GA, 10-VA.  Write 
a program to display the states that recognize at least N 
holidays, where N is input as a number between 5 and 11 inclusive. 
 States must be displayed in the order given above with one space 
in between each state.  Example: 
     INPUT: Enter N: 10 

1.9  Anno Domini is Latin for "in the year of our Lord" and is 
abbreviated as A.D.  In 525 A.D., Pope John I asked the monk 
Dionysius Exiguus to begin a Christian system of dating events, 
starting with the year Dionysius believed Christ was born.  The 
years before the birth of Christ are termed B.C., while the years 
after the birth of Christ are termed A.D.  The following is the 
order of years:  ... 2 B.C., 1 B.C., 1 A.D., 2 A.D., ... with 
Christ's birth being in the year 1 A.D.  Today, we know that the 
monk was in error.  Even though we continue to use his dating 
system, biblical scholars currently believe that Christ was born 
four years earlier than what the monk thought.  Write a program 
that corrects modern dates to account for this change.  Examples: 

     INPUT: Enter date: 4 
            Enter A.D. or B.C.: B.C. 
    OUTPUT: 1 A.D. 
     INPUT: Enter date: 1 
            Enter A.D. or B.C.: A.D. 
    OUTPUT: 5 A.D. 
     INPUT: Enter date: 5 
            Enter A.D. or B.C.: B.C. 
    OUTPUT: 1 B.C. 

1.10  Write a program to display a word diamond for a 7 letter 
word.  The following examples will illustrate the format of a word 
diamond.  Examples: 

     INPUT: Enter word: CONTEST      INPUT: Enter word: PROBLEM 
    OUTPUT:        T                OUTPUT:        B 
                  NTE                             OBL 
                 ONTES                           ROBLE 
                CONTEST                         PROBLEM 
                 ONTES                           ROBLE 
                  NTE                             OBL 
                   T                               B

2.1  Write a program to encode a phrase for the Security 
department.  Each letter in the phrase is to be replaced by the 
letter that precedes it in the alphabet (B becomes A, C becomes B, 
... Z becomes Y), except that the letter A becomes Z.  All other 
characters remain the same.  Example: 

     INPUT: Enter phrase: THIS PERSON IS A THIEF 


2.2  Write a program to determine if a given year is the 
year of our calendar, the year traditionally looked on as the year 
of Christ's birth.  Year 1 began the first decade and the first 
century and the first millennium.  The year 2000 will be the end 
of a decade and a century and a millennium.  Input will be a year 
between 1 and 2000 inclusive.  Output will be all valid 
possibilities of the form XXX OF YYY, where XXX is either 
BEGINNING or END, and YYY is either DECADE, CENTURY, or 
MILLENNIUM.  For more than one line of output, the order must be 

     INPUT: Enter year: 1900          OUTPUT: END OF DECADE 
                                              END OF CENTURY

     INPUT: Enter year: 1991          OUTPUT: BEGINNING OF DECADE

2.3  Bob, Doug, Jackie, and Jose bowl in the NCNB bowling league. 
 Given the scores of each of their 3 games, display each person's 
average and handicap.  If a person has an average over 200, then 
his handicap is 0.  Otherwise, the handicap is calculated by 
subtracting an average from 200 and multiplying the result by 90%. 
 Both the average and handicap must be truncated to a whole number 
when displayed.  Example: 

     INPUT: Enter scores for Bob:    200, 190, 218 
            Enter scores for Doug:   195, 207, 168 
            Enter scores for Jackie: 109, 134, 127 
            Enter scores for Jose:   130, 140, 144 

    OUTPUT: BOB:    AVERAGE = 202  HANDICAP = 0 
            DOUG:   AVERAGE = 190  HANDICAP = 9 
            JACKIE: AVERAGE = 123  HANDICAP = 69 
            JOSE:   AVERAGE = 138  HANDICAP = 55 

2.4  Today we use a Gregorian Calendar, initially set up by Pope 
Gregory XIII in 1582.  Because the previous Julian calendar was 
not an exact representation of a solar year, several days had 
accumulated since its institution.  Therefore, Pope Gregory XIII 
decreed the elimination of 10 days from the year 1582.  For many 
countries October 5, 1582 became October 15, 1582.  However, 
different areas of the world did not adopt the calendar at the 
same time.  Write a program to determine how many days to add to a 
Julian date to convert it to a Gregorian date.  The following 
scale has been devised:

   Add 10 days to Julian dates from 10/5/1582 to 2/28/1700 
   Add 11 days to Julian dates from  3/1/1700 to 2/28/1800 
   Add 12 days to Julian dates from  3/1/1800 to 2/28/1900 
   Add 13 days to Julian dates from  3/1/1900 to 2/28/2100 

Input will be a Julian date of the format MM/DD/YYYY and output 
will be of the format ADD NN DAYS.  Examples: 

     INPUT: Enter date: 09/02/1752    OUTPUT: ADD 11 DAYS 

     INPUT: Enter date: 03/01/1801    OUTPUT: ADD 12 DAYS 

2.5  Sorting is the arranging of elements of a list into order 
based on the value of a particular field within the elements.  
There are several algorithms to accomplish the task of sorting 
including: bubble sort, shell sort, and quick sort.  Each sorting 
algorithm's efficiency depends upon the number of elements to be 
sorted and the particular order in which they are originally 
given.  The average number of comparisons needed to sort a list of 
N elements is given as: 

      N * (N-1) / 2                       for BUBBLE SORT 
      N * ((Log base 2 of N) squared)     for SHELL SORT 
      N * (Log base 2 of N)               for QUICK SORT 

Assuming that the efficiency depends only on the number of 
elements in the list, N, determine the efficiency order of the 
different sorting algorithms and print them from most efficient to 
least efficient.  N will be greater than 2.  Example: 

     INPUT: Enter N: 128 

            SHELL SORT 
            BUBBLE SORT 

2.6  During the summer and fall, NCNB has a golf league for 
employees.  Write a program for a golfer to determine the status 
for each of the 9 holes, given the scores on each hole as input 
and using the pars listed below.  The par is the score standard 
for each hole on a golf course.   Also display the total number of 
strokes the golfer takes and the total par for the 9 holes.  If a 
golfer shoots the standard score for a hole, the status is PAR.  
If on a hole a golfer shoots 1 score below the par, the status is 
BIRDIE.  If the score is 2 below the par, the status is EAGLE.  A 
score of 3 below the par is called a DOUBLE EAGLE.  For scores 1 
and 2 above par, the status is BOGEY and DOUBLE BOGEY 
respectively.  Use the following pars for the holes: 

     HOLE: 1  2  3  4  5  6  7  8  9 
     PAR:  4  3  4  5  4  3  5  4  4 

     INPUT: Enter score for hole 1: 3 
            Enter score for hole 2: 3 
            Enter score for hole 3: 5 
            Enter score for hole 4: 7 
            Enter score for hole 5: 6 
            Enter score for hole 6: 1 
            Enter score for hole 7: 2 
            Enter score for hole 8: 3 
            Enter score for hole 9: 4 

            ----  ---  -----  ------ 
             1     4     3    BIRDIE 
             2     3     3    PAR 
             3     4     5    BOGEY 
             4     5     7    DOUBLE BOGEY 
             5     4     6    DOUBLE BOGEY 
             6     3     1    EAGLE 
             7     5     2    DOUBLE EAGLE 
             8     4     3    BIRDIE 
             9     4     4    PAR 
                  ---  ----- 
                  36    34 

2.7  In 45 B.C. Julius Caesar instituted the use of a calendar. 
The Julian calendar consists of a perpetual cycle of three years 
of 365 days followed by one year of 366 days. However, the exact 
solar year consists of 365 days, 5 hours, 48 minutes, 47.8 
seconds.  Thus, at the end of 1 Julian year, the Julian calendar 
is ahead of a solar calendar that will complete its year in 
another 5 hours 48 minutes and 47.8 seconds. Write a program to 
determine how many days, hours, minutes, and seconds the Julian 
calendar is behind/ahead of an imaginary calendar that is based on 
exact solar years. Assume that both calendars start at the same 
time and a comparison is done at the end of N Julian years, where 
N is input as a natural number less than 2000. Output must have 1 
space between the number and its unit; 2 spaces between the unit 
and the next number. Seconds are displayed using the form ##.#. 

     INPUT: Enter N: 1 
    OUTPUT: 0 DAYS  5 HOURS  48 MIN  47.8 SEC  AHEAD 

     INPUT: Enter N: 2 
    OUTPUT: 0 DAYS  11 HOURS  37 MIN  35.6 SEC  AHEAD 

     INPUT: Enter N: 3 
    OUTPUT: 0 DAYS  17 HOURS  26 MIN  23.4 SEC  AHEAD 

     INPUT: Enter N: 4 
    OUTPUT: 0 DAYS  0 HOURS  44 MIN  48.8 SEC  BEHIND 

     INPUT: Enter N: 5 
    OUTPUT: 0 DAYS  5 HOURS  3 MIN  59.0 SEC  AHEAD 

2.8  In June 1989, Barb and Carolyn founded a suggestion committee 
for the NCNB Systems and Programming Division in Tampa.  In August 
Joe was placed on the suggestion committee.  In September Carolyn 
resigned and Doug took her place.  The committee declared that a 
new person from a waiting list will replace a committee member 
after he/she has served for six months.  With the following 
waiting list, write a program to display the 3 committee members 
for every month that someone is replaced.  The names on a line 
must follow the logical order started in the example.  Input will 
be the last month and year that the suggestion committee meets 
before it disassembles.  The date input will not be later than 5, 


     INPUT:  Enter month, year: 6, 1990 

    OUTPUT:  9/1989 - BARB  JOE  DOUG 
            12/1989 - JACKIE  JOE  DOUG 
             2/1990 - JACKIE  TOM  DOUG 
             3/1990 - JACKIE  TOM  LOVETTA 
             6/1990 - GREG  TOM  LOVETTA

2.9  Write a program to graph both the sine function and the 
cosine function using asterisks.  First, the program is to clear 
the screen.  With dashes {-} for the x-axis and exclamation marks 
{!} for the y-axis, display the axes extending across the entire 
screen with the center (0,0) in the middle of the screen, 
represented by a {+}.  With asterisks {*}, graph the sine function 
varying the x-coordinate from -PI to PI, where (-PI,0) is the left 
most {-} and (PI,0) is the right most {-}.  The top most {!} is 
(0,1) and the bottom most {!} is (0,-1).  Allow the user to press 
any key to clear the screen and display the axes again.  This time 
graph the cosine function with the same coordinate dimensions.  
Allow the user to press any key to clear the screen.  The graphs 
will look similar to the following.  Example: 

     OUTPUT: (Screen clears and the axes is drawn before the 
             graph is drawn from left to right.  Graph will 
             look similar to below, but it extends to the 
             dimensions of the terminal.) 

                                !      ****** 
                                !    ***    *** 
                                !   **        ** 
                                !  **          ** 
                                ! **            ** 
                                !**              ** 
              **              **! 
               **            ** ! 
                **          **  ! 
                 **        **   ! 
                  ***    ***    ! 
                    ******      ! 
     INPUT: (Press any key) 

    OUTPUT: (Screen clears and the axes is drawn before the 
            graph is drawn from left to right- similar to below.) 
                           **  !  ** 
                          **   !   ** 
                         **    !    ** 
                        **     !     ** 
                       **      !      ** 
                     **        !        ** 
                    **         !         ** 
                   **          !          ** 
                 ***           !           *** 
               ***             !             *** 
            ****               !               **** 
     INPUT: (Press any key)    OUTPUT: (Screen clears) 

2.10  A new employee of the NCNB computer programming department 
desires training.  Write a program to produce the following NCNB 
menu of currently available in-house computer courses.  Estimate 
the TOTAL number of hours he/she will spend on training given the 
courses that he/she has selected.  Upon completion of course 
selection, 000-000 is entered.  The screen is then cleared, and 
the course names chosen are displayed again in the order that they 
were selected.  Estimated hours for each course selected must 
appear to the right of the course name: The heading "EST. HOURS" 
starts 26 columns after the first column of the "COURSE NAME," as 
shown in the menu selection.  Also, the TOTAL estimated hours must 
show underneath all the individual course hours in the form:
TOTAL = ##.# - ## HOURS.  Example: 
            COURSE #   COURSE NAME               EST. HOURS 
            --------   -----------               ---------- 
            187-11X    ISPF/PDS FUNDAMENTALS     6.5 - 8 
            187-15X    ISPF/PDS FOR PROGRAMMERS  4.5 - 6 
            220-AXX    JCL FUNDAMENTALS           15 - 20 
            200-AXX    VSAM CONCEPTS               4 - 7 
            123-2XX    MVS/SP/XA VSAM              7 - 11 
            130-11X    CICS/VS SKILLS I            6 - 8 
            130-15X    CICS/VS SKILLS II           4 - 6 
     INPUT: Enter course # (or 000-000 to end): 220-AXX 
            Enter course # (or 000-000 to end): 130-11X 
            Enter course # (or 000-000 to end): 187-11X 
            Enter course # (or 000-000 to end): 000-000 

    OUTPUT: (Screen is cleared) 
            COURSE NAME               EST. HOURS 
            -----------               ---------- 
            JCL FUNDAMENTALS           15 - 20 
            CICS/VS SKILLS I            6 - 8 
            ISPF/PDS FUNDAMENTALS     6.5 - 8 
                             TOTAL = 27.5 - 36 HOURS

3.1  A company would like to use an acronym as a phone number that 
is easy for the public to remember.  They would like a word that 
can be used for the last several digits of their number, where 
each letter corresponds to a particular digit.  Each possible word 
will be 4 or 5 letters long.  Write a program to display all 
possible acronym phone numbers (in the order listed below from 
left to right, top to bottom) for an input number of the format 
XXX-XXXX.  Assume that at least one word will satisfy the 
requirements given the following word list options: 
Use the following letters to correspond to the digits 2 to 9: 
  A B C   D E F   G H I   J K L   M N O   P R S   T U V   W X Y 
    2       3       4       5       6       7       8       9
     INPUT: Enter phone #: 555-3935     OUTPUT: 55J-EWEL 
     INPUT: Enter phone #: 555-2255     OUTPUT: 555-BALL 
3.2  Write a program to select words given a string of letters 
with a wildcard, {*}.  The following words make up the word list: 
The wildcard could come before, after, or between the letters of 
the string.  The program must display all words in the list (in 
order from left to right, top to bottom) separated by 2 spaces 
that are of the form input, where the wildcard could represent 0 
to 10 letters.  The words may be in any order.  If no words are 
found then display the message NO WORDS FOUND.  The program is to 
continue to display words and to accept as input a string with a 
wildcard until a string is entered without a wildcard.  Example: 
     INPUT: Enter string: CREAT*
     INPUT: Enter string: *TION       INPUT: Enter string: *ATER
     INPUT: Enter string: E*Y         INPUT: NO
    OUTPUT: EVERYBODY  EMPTY         OUTPUT: (Program terminates)

3.3  Three local cross country teams compete in a double dual 
race.  Each team consists of seven runners, but only the first 
five finishers of a team contribute to that team's score.  As the 
runners cross the finish line, gasping for breath, the judge 
writes the INITIAL of the runner's team name and the NUMBER 
indicating the runner's finishing position, e.g. 1 for 1st, 2 for 
2nd and so on.  To find the score for teams A and B and to decide 
which of the two wins, the scorekeeper temporarily eliminates all 
of C's positions, and then repositions the runners from A and B 
into places 1 through 14.  The team's score consists of the sum of 
the places of their first five runners.  The lower team score 
wins.  If there is a tie then the team whose sixth runner crossed 
the finish line first is the winner. 

Write a program that computes the score for each pair of three 
teams and determines the winner of each pair (pairs may be 
displayed in any order).  The program must allow the user to 
assign all 21 runners' team INITIAL to finishing places.  Team 
initials can be any letter in the alphabet.  Example:  

     INPUT: Place 1: A                     |   Example of 
            Place 2: B                     |   repositioning 
            Place 3: A                     |   teams A and B: 
            Place 4: B                     | 
            Place 5: A                     |   1: A 
            Place 6: B                     |   2: B 
            Place 7: C                     |   3: A 
            Place 8: C                     |   4: B 
            Place 9: C                     |   5: A 
            Place 10: C                    |   6: B 
            Place 11: B                    |   7: B 
            Place 12: A                    |   8: A 
            Place 13: C                    |   9: B 
            Place 14: B                    |  10: B 
            Place 15: C                    |  11: A 
            Place 16: B                    |  12: A 
            Place 17: A                    |  13: B 
            Place 18: A                    |  14: A 
            Place 19: C 
            Place 20: B 
            Place 21: A 
             TEAM B: 28 POINTS 
             TEAM B WINS! 
             TEAM A: 25 POINTS 
             TEAM C: 31 POINTS 
             TEAM A WINS! 
             TEAM B: 24 POINTS 
             TEAM C: 31 POINTS 
             TEAM B WINS! 

3.4 Within NCNB's Application Systems Division, there are many 
programming teams consisting of 2 to 8 programmers and 1 team 
leader.  Suppose that NORM is a team leader in charge of 3 
programmers: AL, DOUG, and JAN.  Norm has been given 30 programs 
(numbered 1 through 30) to distribute amongst his employees.  Al 
is given all programs divisible by X, and Doug is given all 
programs divisible by Y.  Jan is given all programs divisible by 
Z, and Norm takes the rest of the programs that were not assigned 
to anyone and will work on some himself or he will redistribute 
some later.  Given X, Y, Z as different input numbers between 2 
and 10 inclusive, write a program to display those program numbers 
shared by all 3 of the programmers, those shared between only 2, 
and those assigned solely to 1 person.  If no programs are 
assigned exclusively to one particular group, then display NONE 
instead of program numbers.  The output must be in the same format 
as shown: eight lines, with numbers in increasing order.  

     INPUT: Enter X, Y, Z: 2, 3, 5 
            AL AND DOUG = 6 12 18 24 
            AL AND JAN = 10 20 
            DOUG AND JAN = 15 
            AL = 2 4 8 14 16 22 26 28 
            DOUG = 3 9 21 27 
            JAN = 5 25 
            NORM = 1 7 11 13 17 19 23 29 
      INPUT: Enter X, Y, Z: 2, 6, 9 
     OUTPUT: AL, DOUG, AND JAN = 18 
             AL AND DOUG = 6 12 24 30
             AL AND JAN = NONE 
             DOUG AND JAN = NONE 
             AL = 2 4 8 10 14 16 20 22 26 28 
             DOUG = NONE 
             JAN = 9 27 
             NORM = 1 3 5 7 11 13 15 17 19 21 23 25 29 

3.5  The numbers 1 through 8 and a blank are randomly placed in a 
3 X 3 array on the screen.  For example: 

                    5  8  3 
                       4  1 
                    6  2  7 

Write a program so that when a key from 1 - 8 is pressed, the 
corresponding number on the screen slides horizontally or 
vertically to the adjacent blank location.  If a key is pressed 
that is not horizontally or vertically adjacent to the blank, the 
computer does nothing.  (For example: in the above diagram, only 
the 3, 1, and 7 can be moved.)  The user can repeat this process 
of sliding numbers until the digit 9 is pressed, which causes the 
program to terminate.Example: 
    OUTPUT:  4  3  1 
             2  8  5 
                7  6 
     INPUT: (Press 2)
    OUTPUT:  4  3  1 
                8  5 
             2  7  6 
     INPUT: (Press 8) 
    OUTPUT:  4  3  1 
             8     5 
             2  7  6 
     INPUT: (Press 6)
    OUTPUT: (No change) 
     INPUT: (Press 9)
    OUTPUT: (Program terminates) 

3.6  Write a program to simulate a chess game between two players. 
Display a chess board with the white chess pieces at the bottom of 
the board (designated by a leading W), and the black pieces at the 
top of the board (designated by a leading B).  The board is set up 
according to the international chess notation: a letter of the 
alphabet designates vertical columns, and a number designates 
horizontal rows.  The board must be displayed as below.  The 
computer allows WHITE to move first, and then allows BLACK to 
move.  The computer continues to alternate moves until a king is 
captured.  The White king is designated as WK and the black king 
is designated as BK.  The user enters a valid move in the format 
L#-L# where L is one of the letters (A, B, C, D, E, F, G, H) and # 
is one of the digits (1, 2, 3, 4, 5, 6, 7, 8).  The piece 
occupying the coordinate of the first L# is moved to the 
coordinate of the second L#.  If a piece is moved onto the 
opponent's square, the opponent's piece is removed.  If a piece 
takes over an opponent's king, then print CHECK MATE, CCCCC WON 
(where CCCCC is either WHITE or BLACK).  Only valid moves will be 
entered, and neither castling nor the "en passant" move will be 
done.  No "check" warning is given in this game.  Example: 
    OUTPUT: BR1 BK1 BB1 BQ  BK  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5 BP6 BP7 BP8  !  7 
                                             !  6 
                                             !  5 
                                             !  4 
                                             !  3 
            WP1 WP2 WP3 WP4 WP5 WP6 WP7 WP8  !  2 
            WR1 WK1 WB1 WQ  WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
     INPUT: Enter white move: E2-E4 

    OUTPUT: BR1 BK1 BB1 BQ  BK  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5 BP6 BP7 BP8  !  7 
                                             !  6 
                                             !  5 
                            WP5              !  4 
                                             !  3 
            WP1 WP2 WP3 WP4     WP6 WP7 WP8  !  2 
            WR1 WK1 WB1 WQ  WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
     INPUT: Enter black move: F7-F6 

    OUTPUT: (continued on next page) 

(output continued)

    OUTPUT: BR1 BK1 BB1 BQ  BK  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5     BP7 BP8  !  7 
                                BP6          !  6 
                                             !  5 
                            WP5              !  4 
                                             !  3 
            WP1 WP2 WP3 WP4     WP6 WP7 WP8  !  2 
            WR1 WK1 WB1 WQ  WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
     INPUT: Enter white move: D1-H5 

    OUTPUT: BR1 BK1 BB1 BQ  BK  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5     BP7 BP8  !  7 
                                BP6          !  6 
                                        WQ   !  5 
                            WP5              !  4 
                                             !  3 
            WP1 WP2 WP3 WP4     WP6 WP7 WP8  !  2 
            WR1 WK1 WB1     WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
     INPUT: Enter black move: B8-C6 

    OUTPUT: BR1     BB1 BQ  BK  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5     BP7 BP8  !  7 
                    BK1         BP6          !  6 
                                        WQ   !  5 
                            WP5              !  4 
                                             !  3 
            WP1 WP2 WP3 WP4     WP6 WP7 WP8  !  2 
            WR1 WK1 WB1     WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
     INPUT: Enter white move: H5-E8 

    OUTPUT: BR1     BB1 BQ  WQ  BB2 BK2 BR2  !  8 
            BP1 BP2 BP3 BP4 BP5     BP7 BP8  !  7 
                    BK1         BP6          !  6 
                                             !  5 
                            WP5              !  4 
                                             !  3 
            WP1 WP2 WP3 WP4     WP6 WP7 WP8  !  2 
            WR1 WK1 WB1     WK  WB2 WK2 WR2  !  1 
             A   B   C   D   E   F   G   H 
            CHECK MATE, WHITE WON 

3.7  Write a program to determine the date of Easter and the date 
of Lent for a given year between 1970 and 2009 inclusive.  Easter 
falls on the first Sunday following the arbitrary Paschal Full 
Moon, which does not necessarily coincide with a real or 
astronomical full moon.  The Paschal Full Moon occurs on one of 
the following 19 dates corresponding to a key.  The key is the 
remainder obtained by dividing the year by 19. 
      Key  Date               Key  Date 
      ---  ----               ---  ---- 
       0   April 14           10   March 25 
       1   April 3            11   April 13 
       2   March 23           12   April 2 
       3   April 11           13   March 22 
       4   March 31           14   April 10 
       5   April 18           15   March 30 
       6   April 8            16   April 17 
       7   March 28           17   April 7 
       8   April 16           18   March 27 
       9   April 5 
Therefore, the key for the year 1990 is 14 (because 1990 / 19 = 
104 remainder 14), and the Paschal Full Moon occurs on April 10.  
Since April 10, 1990 is a Tuesday, Easter Sunday is April 15.  
Note, if the Paschal Full Moon falls on a Sunday, Easter is the 
following Sunday.  The earliest Easter can fall is March 23, and 
the latest is April 25.  Lent begins on Ash Wednesday which comes 
40 days before Easter, excluding Sundays (46 days including 
Sundays).  Note, January 1, 1970 is a Thursday, and every year 
between 1970 and 2009 that is divisible by 4 is a leap year.  
     INPUT: Enter year: 1970 
            LENT IS ON FEBRUARY 11 
     INPUT: Enter year: 1996 
            LENT IS ON FEBRUARY 21 
     INPUT: Enter year: 2000 
            LENT IS ON MARCH 8 

3.8  Write a program to keep score for a bowler.  Input will be 10 
frames of numbers.  Output will be the scoring of each frame, as 
shown below in the example.  The standard method of scoring will 
be used in this program. 
     In each frame the bowler has at most two chances to roll down 
all 10 pins.  If the bowler does not knock down all the pins in 
that frame, then his score is added to the number of pins that he 
previously knocked down.  (Note: the bowler's score starts out as 
     For the first 9 frames, if the bowler knocks all 10 pins down 
on the 2nd roll (indicated by a /) then his score for that frame 
is his previous score + 10 + the number of pins that he knocks 
down on his next roll in the next frame.  If he rolls all the pins 
down on his 1st ball of a frame (indicated by an X) then he gets 
10 + the total number of pins that he knocks down on the next 2 
rolls.  A new frame is started after 2 balls are rolled or all ten 
pins are knocked down on the 1st ball. 
     In the 10th frame, the bowler is allowed at most three rolls, 
depending upon his first and second rolls.  If he gets all the 
pins down on the 1st roll then his score will be his previous 
score plus 10 plus the number of pins he knocks down on his next 2 
rolls.  If he knocks all 10 pins down after 2 rolls, his score 
will be his previous score + 10 + the number of pins he knocks 
down on his next roll.  Frame inputs are right justified and the 
score is left justified in each frame.  Example: 
     INPUT: Enter frame 1: 7/ 
            Enter frame 2: X 
            Enter frame 3: 62 
            Enter frame 4: X 
            Enter frame 5: X 
            Enter frame 6: 8/ 
            Enter frame 7: 63 
            Enter frame 8: X 
            Enter frame 9: X 
            Enter frame 10: X9- 

(Note: 62 indicates that 6 pins were knocked down on 1st roll 
         and 2 pins were knocked down on 2nd roll; 
     / indicates all remaining pins knocked down on 2nd roll; 
     X indicates 10 pins knocked down on the 1st roll; 
     - indicates 0 pins knocked down.) 
    OUTPUT: -1- -2- -3- -4- -5- -6- -7- -8- -9- -10- 
             7/!  X! 62!  X!  X! 8/! 63!  X!  X!X9-! 
            20 !38 !46 !74 !94 !110!119!149!178!197! 

3.9  Write a program to solve a system of N equations with N 
unknowns.  The program will first accept a value for N between 2 
and 4 inclusive.  For each equation the program should accept the 
values for the N coefficients followed by the constant.  Each 
given system of equations will have one unique solution whose 
values will be integers.  A possible algorithm to be used to solve 
an NxN system of equations is shown to the right of the example 
input/output.  Examples: 
INPUT: Enter N: 3           |  2x + 4y + 6z = 4    (Divide by 2) 
Enter coefficients for row1 |  2x +  y +  z = 3 
Co1: 2                      |  -x + 2y +  z = 2 
Co2: 4                      | 
Co3: 6                      |  1  2   3   2 
Enter constant: 4           |  2  1   1   3   (Subtract 2*Row1) 
Enter coefficients for row2 | -1  2   1   2 
Co1: 2                      | 
Co2: 1                      |  1  2   3   2 
Co3: 1                      |  0 -3  -5  -1 
Enter constant: 3           | -1  2   1   2   (Subtract -1*Row1) 
Enter coefficients for row3 | 
Co1: -1                     |  1  2   3   2 
Co2: 2                      |  0 -3  -5  -1   (Divide by -3) 
Co3: 1                      |  0  4   4   4 
Enter constant: 2           | 
                            |  1  2   3   2 
OUTPUT: (1, 2, -1)          |  0  1  5/3 1/3 
                            |  0  4   4   4   (Subtract 4*Row2) 
                            |  1  2   3   2 
INPUT: Enter N: 2           |  0  1  5/3 1/3 
Enter coefficients for row1 |  0  0 -8/3 8/3  (Divide by -8/3) 
Co1: 1                      | 
Co2: 1                      |  1  2   3   2 
Enter constant: 1           |  0  1  5/3 1/3  (Subtract 5/3*Row3) 
Enter coefficients for row2 |  0  0   1  -1 
Co1: 2                      | 
Co2: 3                      |  1  2   3   2   (Subtract 3*Row3) 
Enter constant: 6           |  0  1   0   2 
                            |  0  0   1  -1 
OUTPUT: (-3, 4)             | 
                            |  1  2   0   5   (Subtract 2*Row2) 
                            |  0  1   0   2 
                            |  0  0   1  -1 
                            |  1  0   0   1 
                            |  0  1   0   2 
                            |  0  0   1  -1 

3.10  Write a program to solve cryptorithms (a puzzle in which the 
letters of the alphabet are written in a computational format).  
The object is to determine which digit corresponds to each letter 
in the puzzle to satisfy the computation.  Input will be two 
2-letter addends and a 3-letter sum.  The program will generate a 
numeric solution for each of the letters used.  The judging 
criteria will be such that there will always be at least one 
solution.  Only the letters A, B, C, D, and E may be used in the 
input, and the leading letter may not be 0.  Example: 

     INPUT: Enter first addend:  AB 
            Enter second addend: BC 
            Enter sum: DDB 

    OUTPUT: (Only one of the following solutions must be shown)
            A = 2      3      4      5         6      7      8
            B = 9  or  8  or  7  or  6     or  5  or  4  or  3 
            C = 0      0      0      0         0      0      0
            D = 1      1      1      1         1      1      1