1-2-3-4 POW
Problem Statement
Create 1-2-3-4 expressions to equal numbers in between 1 and 25. For each equation you have to use each of the digits 1, 2, 3, 4 only once. Here are some other rules we were told to follow: we can use any basic operations + - / *, we are allowed to use exponents, we can use radicals, you may use factorials, parentheses and brackets and we were allowed to juxtapose two or more digits to form numbers.
Procedure
For this specific problem my procedure was very simple. I was going to write down numbers one through twenty-five and try to figure out 1-2-3-4 expressions that equal the numbers in between. So I started by writing down the ones I did know or just created off the top of my head, for example 10 = 1+2+3+4 or 25= 4*3*2+1. I worked from there by trying to mix random operations with numbers in different orders. If you look at the pictures there is a little pattern or that is what it seems to me, they all end either in -1, *1, or +1. I did have a little bit of assistance from my cousin who helped me find this “pattern” but I didn't quite know how to put it in my own words, also I am not 100% sure that this is a pattern and if it is, is it consistent or not.
Solution
Below on the right side is a picture of my solutions. These are all the 1-2-3-4 expressions I got for numbers 1-25. I know these are correct answers because they follow all the rules and guidelines and were double checked by me and my relatives. Also some of these expressions aren't the same as the ones in the picture above and this is because I found multiple expressions that follow the rules and equal the same number.
Self-Assessment and Reflection
Through this project I learned mostly about test my thoughts out and just giving it a try. I learned this because I wasn't afraid to try out this craziest expression because I knew the worst thing that could happen would be that my expression would not equal the numbers I was looking for, and I was okay with that. This is also a Habit of a Mathematician I have learned to develop, Conjecture and Test. I mainly talked about it above but this entire problem for me was conjecture and test, coming up with random expressions and testing them to find similarities and patterns. If I were to grade myself on this assignment, out of 10, I would give myself a 9. I gave myself a 9 because I feel that I did the assignment well, followed all the rules and guidelines, very well presented, but there is also room for improvement. I feel that I couldn't expanded my research in this problem by trying to find more expressions to the numbers 1-25. This would be great to expand my knowledge in mathematics.