1 DIAMOND

Write a program that will ask the user for a whole number N between 3 and 10 and print a diamond of size N as shown in the sample run.

Test your program for N = 4 and N = 7.

Sample Run

ENTER A WHOLE NUMBER BETWEEN 3 AND 10: 4

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2. PATTERNS

Examine the pattern of the numbers in the triangle of size 7 shown below.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 ?? ?? ?? ?? 7 1

What should the last row should be? Write a program that will generate this triangle for any number of rows from 1 to 10. Test your program for N=7 and N=10.

Hint: Look at the previous row to get values for the current row.

3 DIE TOSS

A die is a cube with 6 equal sides numbered {1, 2, 3, 4, 5, 6}. Galileo performed the experiment of tossing three fair dice and summing the numbers that appear. He was interested in knowing which outcome was more likely:

1) Summing to 9 or

2) Summing to 10.

Write a program to repeat Galileo's experiment N times and compare the number of times the sum is 9 with the number of times the sum is 10. Conclude which sum is more likely to appear. Test your program for N=400.

Sample Run

Enter the number of trials N: 400

The sum was 9: 45 times.

The sum was 10: 47 times.

this experiment implies that

getting a 10 is more likely than getting a 9

in the toss of three dice.

Note: Your experiment will more than likely have different numbers and could trigger a different conclusion.

4. REVERSE

Write a program that asks the user for a sentence and prints the sentence reversing the words that are separated with "and". Thus ... BILL AND JIM ..... changes to ......JIM AND BILL..... . Assume all of the words are entered in upper case.

Test your program with the follow sentence:

you and I are going to the STORE to buy a hat and coat.

Sample Run

ENTER A SENTENCE: YOU AND ME BABY.

ME AND YOU BABY.

5. CONSECUTIVE SUMS

Write a program that will find and count the ways that a positive whole number can be written as the sum of two or more consecutive positive whole mumbers.

Sample Run

ENTER A WHOLE NUMBER : 45

THE CONSECUTIVE SUMS ARE:

45 = 1+2+3+4+5+6+7+8+9

45 = 5+6+7+8+9+10

45 = 7+8+9+10+11

45 = 14+15+16

45 = 22+23

NUMBER OF CONSECUTIVE SUMS = 5