If Actual arrangement

21222,22122,22212

Logicians assumed cases

11222,12122,12212 in this case last person would have said that he has 2 hats (since least count + max 2 hats on head) evaluates to two hats on last head

21222,22122,22212 but in assumed arrangement since last person didnt said anything first person can predict he has 2 hats

in this way game completes

But if actual arrangment is

12222,22221 then first and last logicians may assume following arrangement as well

12221,12221 respectively so game do not completes

If Actual arrangement

21222,22122,22212

Logicians assumed cases

11222,12122,12212,21122,21212,22112 in this case last person would have said that he has 2 hats (since least count + max 2 hats on head) evaluates to two hats on last head

21222,22122,22212 since in assumed arrangement since last person didnt said anything first person can predict he has 2 hats

in this way game completes

But if actual arrangment is

12222,22221 then first and last logicians may assume following arrangement as well

12221,12221 respectively so game do not completes