Pow 2 1-2-3-4 Puzzles

Pow 2 1-2-3-4 Puzzles

Problem Statement:

The situation is that you are given the numbers 1,2,3, and 4 to make arithmetic expressions for the numbers 1-25.

The facts are that you may use exponents, radicals, factorials, parentheses, and brackets. You may juxtapose the numbers, too. You can only use the numbers 1,2,3,and 4 exactly once in each expression. You may also use the basic addition, subtraction, multiplication and division.

My task is to create as many 1-2-3-4 arithmetic expressions as I can for the numbers 1-25.

Process:

To figure out this problem, all I did was kind of "play" with the numbers. I, at the beginning, only used addition, subtraction, and multiplication and found expressions for the numbers 2,3,4,and 5. Then I started using radicals, factorials, and exponents. I didn't know what to do with factorials, so I called my friend Kenna and she explained it to me and helped me understand. By the end , I was getting kind of creative, using 2 or 3 of the radicals, factorials, or exponents in one expression. I had to get more creative because the expressions needed to be more complicated so I could get the answer I needed.

I didn't find any patterns to help me figure out this problem. I thought that finding the expressions was pretty easy once I got the hang of it.

At one point, I realized I had forgotten to use the order of operations. This was a bit of a problem. I had to backtrack and check all of my expressions to make sure they were still going to work. I lost a lot of time because of this mistake, but I fixed it.

Solution:

All of my expressions are my solutions to this problem. I know

my answers are correct and complete because I know I followed all of the rules the problem said to follow. I've listed these rules in my problem statement. My expressions are attached on a separate sheet of paper.

Extensions:

( The following are variations to this problem)

Extensions - 1

In this problem, the task is to create 75 arithmetic expressions for the numbers 1-25, using the numbers 1-10 in the expressions. Please follow the following rules:

1.You must follow the order of operations.

2.You may use addition, subtraction, multiplication, and division.

3.You must use factorials at least 10 times.

4.You must use radicals at least 10 times.

5.You must use exponents at