Lewis Carroll's famous monkey question

You might know Lewis Carroll was the author of "Alice in Wonderland" did you know he was also a physics professor at Oxford.

The problem goes like this.
you have a frictionless pulley with a rope over the top. On each side of the rope hangs a monkey of equal mass that balances the load. He asked the question what happens when one of the monkies decides to climb the rope?

I have long been troubled by the accepted answer that the monkey that climbs will fall to his death.

Thinking logically he mas does not change so the equilibrium remains intact. the change in tension of the rope serves to shorten the distance between the two monkies. the correct answer in my opinion is that both monkies rise the climbing monkey moves half as high as the amount of rope he pulls, provided he is strong enough to lift both of their weight.

Is this an example of a rising tide lifts all ships...

This question has been long debated let it continue I guess