I had always thought the idea of the third twin was to establish that time dilation was not caused by acceleration. The third twin gives us the same result as if one of the twins had accelerated, but since none of the twins had to accelerate to provide this answer, it proves that acceleration is not the cause.
But apparently RJBeery had a different interpretation of what the third twin's purpose was. He thought the third twin was supposed to establish which of the first two twins was actually younger than the other. So his thought experiment was designed to demonstrate that no matter how many twins you use, you still don't get a definitive answer as to which of the first two twins was actually younger than the other.
That is because:
a. RJ messed up his calculations
b. RJ does not understand closing speed
c. RJ does not understand the notion of proper time , let alone the invariance of proper time
None of the above stops him from piling new errors on top of the older ones.