Each individual who successfully solves at least one problem will receive a 100 on a lab grade. In addition, the top three individual will receive the following extra credit:

- First place: 100 extra points toward the labs.
- Second place: 50 extra points toward the labs.
- Third place: 25 extra points toward the labs.

Create a lab12 subdirectory in the 1440 directory of one of the group members. Put all work for lab12 in that subdirectory. As soon as you think you have solved a problem correctly, tell me the name of the file containing the program and I will move it to my directory to check it.

**1)** Write a program that will take
as input a decimal digit, i.e., 0-9, and draw a triangle of the given decimal
digit height with each column containing the digit corresponding to the
number of digits in the column. For example, if the user enters 5, the
following picture would be drawn:

5 54 543 5432 54321

2)Problem 5, p. 437 of your text. Write a program that accepts a year written as a four-digit Arabic (ordinary) numeral and outputs the year in Roman Numerals. Important Roman numerals are: V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1000. Recall that some numbers are formed by using a kind of subtraction of one Roman "digit"; e.g., IV is 4 produced as V minus I, XL is 40, CM is 900, etx. A few sample years: MCM is 1900, MCML is 1950, MCMLX is 1960, MCMXL is 1940, MCMLXXXIX is 1989. Assume the year is between 1000 and 3000.

Write a program that asks for the user's height, weight, and age, and then computes clothing sizes according to formulas:

- Hat size = weight in pounds divided by height in inches and all that multiplied by 2.9.
- Jacket size (chest in inches)=height times weight divided by 288 and then adjusted by adding 1/8 of an inch for each 10 years over age 30. (Note that the adjustment only takes place after a full 10 years. So, there is no adjustment for ages 30 through 39, but 1/8 of an inch is added for age 40.)
- Waist in inches= weight divided by 5.7 and then adjusted by adding 1/10 of an inch for each 2 years over age 28. (Note that the adjustment only takes place after a full 2 years. So there is no adjustment for age 29, but 1/10 of an inch is added for age 30.)

Enter a four digit number: 5678 5 6 7 8

5)Write a program that asks the user for the number of characters, n, in a string and then asks the user to input that many characters. Finally, the program generates all permutations for the string of length n and outputs each permutation to the screen.

- Following is an example:

Please enter the number of characters: 3 Please enter a string of length 3: cat Here are the permutations of cat: cat cta tca tac act atc(Hint: The number of permutations of a string is equal to the factorial of the length of the string.)

1) 0 < a < b < c; and

2) c^{2 }= a^{2 }+ b^{2}.

Write a program that takes 3 integers as input and reports whether
they form a Pythagorean Triple.

Example 1: Enter a: 3 Enter b: 4 Enter c: 5 A Pythagorean Triple. Example 2: Enter a: -3 Enter b: 4 Enter c: 5 Not a Pythagorean Triple.