Add together values in corresponding positions of the top two crosses, and put the result in the lower left cross.

1 + 1 = 121 = 1x1 1+1 1x1

Given 

Here the given Number Puzzle follows a pattern that, Sum of the numbers on the corners on the two squares is same and is equal to 54.

In each triangle, multiply the lower two numbers together and add the upper number to give the value at the centre.

Here the puzzle follows the logic that

If you add all the terms of the LHS of equality, then the last letter of the sum written in words would give you the RHS.

From all the hints given, 

Logic is

In the given number puzzle,

The given puzzle follows a logic that,

As you move down, the numbers represent multiples of 12,subtracting 1 for the first step,adding 2 for the second, subtracting 3 for the third, adding 4 for the next ect.ect

The given number puzzle can be soved in two ways.

Observe that in each column, square of sum of digits in the first row = Respective second row elements.