Senior Division 1986
1.  TENT GRAPH
Write a program that will generate and print out Tent Graphs like the 
one shown in the sample run for any size N between 2 and 10. Test 
your program for N= 6 & 10.  The fewer PRINT statements you  use, 
the higher your solution will be rated.

Sample Run
ENTER A VALUE FOR N: 6


	!    *
	!   * *
	!  *   *
	! *     *
	!*       *
	*---------* 

2. STEPPING STONES
A set of stepping stones with lengths 1, 1/2, 1/3, 1/4, 1/5 
.......(continuing in this pattern)  are available -- one step for each size. 
It takes at least four steps placed in a stair-step fashion with decreasing 
step-size (as shown below) for the total height to exceed 2. Three steps 
are not enough; four is the minimum number of steps necessary to 
equal or exceed the height of 2.




Write a program that computes and prints a table showing the 
minimum number of steps necessary to equal or exceed a given height 
from 1 to 8. Print out a table in the following format shown in the 
sample run.


Sample Run

HEIGHT	STEPS
--------------------
1		1
2		4
3		11
4		31
5		83
6		227
7		616
8		????
	

3. DART BOARD
Darts thrown at a dart board land in different REGIONS of the board 
and a VALUE or score is assigned.  The total score is the sum of the 
values scored for each toss. The two views of the dart board below 
show the regions on the board and the corresponding values or scores. 



Assume that regions 2, 3, and 4 are each three times more likely to be 
hit as region 1. Write a program that simulates the tossing of darts 
until the score first equals or exceeds 1000 -- when the game ends. Use 
the random number generator below to simulate the tossing of the 
darts.

SEED VALUES (for the Random Number Generator)
	J=2^7+3 : M=2^15: L=1
	SUBROUTINE: R is a Random Region Generator on [0 1] .
	Begin the generator with the seed L=1.
	L=J*L-M*INT(J*L/M)
	R=L/M
	RETURN

The regions hit by darts MUST be simulated by using the Random 
Number Generator shown above. 

Print out a report as shown in the sample run.

Sample Run

	REGION	HITS	POINTS
	 1	  32	 224
 	 2	  75	 375
	 3	 103	 309
	 4	  93	  93
	       TOTAL = 1001


4. WORD CHECKER
Write a program that asks the user to enter any upper-case sentence 
(assume less than 250 characters in length) and checks it against the 
words in the DICTIONARY shown below. All words not found in the 
Dictionary must be printed out in a table arranged alphabetically with 
no duplicates. Assume that no commas are used in the sentence 
entered. Test your program with the following sentence (the spaces 
around the word ALL are intended and should be entered). Your 
program should handle the spaces properly and should not count them 
as words.Test your program with the sentence:

NOW IS DE TIME FOR     ALL    GOUD PRBLEM SOLVERS TO 
SOLVE  THIS PRBLEM.

DICTIONARY WORDS:
A, ALL, FOR, GOOD, IS, NOW, PROBLEM, SOLVE, SOLVERS, 
THIS, TIME, TO, WRITE

Sample Run
ENTER A SENTENCE IN UPPER-CASE 

? NOW IS DE TIME FOR    ALL   GOUD PRBLEM SOLVERS TO 
SOLVE DHIS PRBLEM.

WORDS NOT FOUND IN DICTIONARY
DE
DHIS
GOUD
PRBLEM

	
5. 6X6 CHECKER CHALLENGE
Look at the 6X6 checkerboard below and try to place six checkers on 
the board so that one and only one is placed in each row, each column, 
and there is never more than one in any diagonal.




The solution shown above is described by the digits 2 4 6 1 3 5, which 
gives the column positions of the checkers for each row from 1 to 6.

ROW         	1 2 3 4 5 6
COLUMN 	2 4 6 1 3 5 

This is one solution to the 6X6 Checker Challenge. Write a program 
that searches and finds all unique solutions to the 6X6 Checker 
Challenge. Print out the solutions using the column notation described 
above and count the total number of solutions found.

Sample Run

2 4 6 1 3 5
3 6 2 5 1 4
4 1 5 2 6 3
? ? ? ? ? ?

THERE ARE ? SOLUTIONS TO THE 6X6 CHECKER 
CHALLENGE.


                                     ICPSC 1986
                             Senior Division Problems




