1, 2, 3, 4 number problem

Question

you are given the digits 1, 2, 3, and 4. You have to keep them in that order, but you are allowed to add, subtract, multiply and divide to simplify them. You may also use exponents, parenthesis and square roots to simplify the numbers in an expression. Your task is to create as many 1-2-3-4 expressions as you can for the numbers from 1 to 25. Remember, in each expression, you must use each of the digits 1, 2, 3, and 4 exactly once in order.

Answer 1

These are not the only combinations:

 

1            1²³⁴

2            1+2+3-4

3            12-3^√4     

4            1+2-3+4

5            1+2³-4

6            1-2+3+4

7            1+2³-√4

8            (12/3)+4

9            -1-2+(3*4)

10          1+2+3+4

11          -1+2³+4

12          1+2+3^√4

13          1+2³+4

14          (1*2)+(3*4)

15          1+2+(3*4)

16          1*2³*√4

17         -1+(2*3^√4)

18         -1+23-4

19         12+3+4

20         1+23-4

21         12+3^√4

22         -12+34

23         -1+(2*3*4)

24         1*2*3*4

25         1+(2*3*4)

 

and no, it wasn't easy ... See if you can come up with some different combinations.