How can you go from the number 11 to 25 by only multiplying by 2 or decreasing by 3 in a minimum number of steps?
Lets play this game backwards, start at 25 with the valid operations of "increase by 3" or "divide by 2".
And since 11 is less than 25 I will use a simple rule of "divide by 2 if even else increase by 3".
Then going for six steps yields 25, 28, 14, 7, 10, 5, 8. This is good, all I need now is to deviate from my rule for the last operation and add 3.
To go back to the original problem then the desired sequence is 11, 8, 5, 10, 7, 14, 28, 25.
Pencil and Paper
