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