- Author: Graham Mitchell
- Filename: NumberPuzzles4.java

### Number Puzzles IV: A New Hope

Use nested `for`

loops to find four positive integers
whose sum is 45, and such that the first plus 2, the second minus 2, the
third multiplied by 2, and the fourth divided by 2 are all equal.

Please note that these four numbers are **integers**,
and not necessarily just digits. In this problem, we are no longer
finding a single four-digit number; we are finding four separate numbers.
However, since we are trying to generate all possible combinations, the
procedure should be the same.

For those of you having trouble with the English on this one (I've
noticed that students really don't like word problems), here's what
that means.

- The output of your program should be four numbers. They
won't be negative numbers.
- When you add the four numbers, they add up to 45.
- If you add 2 to the first number, you get the same answer as
if you had subtracted 2 from the second number.
- If you multiply the third number by two, you also get the same
answer.
- If you divide the fourth number by two, you also get the same
answer.

The following mathematical statments are also true about these numbers:

`A + 2 = B - 2 = C × 2 = D ÷ 2`

and

©2013 Graham Mitchell

This assignment is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License.