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The solution for this puzzle is simple for level 1 and 2. As for level 1, you would look at the differences between the numbers and all the differences should turn out the same. The differences between the numbers is the times table. For example: if the difference between the numbers was 4, the times table would be the 4 times table. From there you can work out if it is being shifted up or down and by how much if you find the difference between the shifted times table number and the actual times table number. For example: If we know the times table is the 4 times tables, we would do the first shifted times table number minus 4 (4*1).
As for level 3 and 4 it is slightly trickier. As the shifted numbers are not in order it makes it harder to work out. Firstly, you can find the difference between the 2 smallest shifted numbers. Find out the multiples in those times tables(difference between the smallest shifted numbers) and see if any multiples dont have much a difference from the shifted numbers given. Remember that the shifted number cannot be bigger than the times table number itself. If the difference between the multiple of the times table and the shifted number is smaller than the times tables number itself then the answer would be correct.