Question 189
On the left scale of a balance 4 weights weighing $22$, $24$, $26$, $28$ grams each are placed and on the right scale 4 weights weighing $23$, $25$, $27$, $29$ grams each are placed. This balance gets tilted toward the side having heavier total weight, and settles in equilibrium position when the total weights of both sides are equalized. Suppose we repeat a procedure of removing a weight from the scale on the tilted side, until the equilibrium is reached. How many different ways of removing the weights are there if the equilibrium is reached only when all the weights are removed?