POW

Problem Statement-
Create 1-2-3-4 expressions for each of the numbers 1-25. If you find more than one answer for a number write that down too. In each case, the expression must use the numbers 1, 2, 3, & 4 exactly once.

Process-
First I just tried simple addition to figure out the problem.

1+2+3+4= 10
21+34=55
41+32=74

Then I realized my numbers were too big, so I started to add parenthesis and multiplication to my problem.
2+3+4x1=9
(2+3+1)4=24
4x3+1+2=15
4x3x1+2=14
4x2+1+3=12
4x2x3+1=25
(4x1)+(2x3)=10
(4x1+2)x3=18

Then I started adding subtraction to my problem.
4 -3+2-1=2
4 -1x3+2=11
4 -1x2+3=5
4 -3+2+1=4
3-1+2x4=8
4 -3+2-1=2
4 -2-1+3=4
41-32=9
23-14=9
34-12=22

This gave me most of my answers after I played around a bit.

Solution-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

Extensions-
To change the problem I could ...