Each person has to roll their die a number approaching infinity times, then the reported means will be normally distributed. Now you will almost always get some

Each person has to roll their die a number approaching infinity times, then the reported means will be normally distributed. Now you will almost always get something quite indistinguishable from normal with n=50 throws, but not with n=1. If you plot the means of the 300 dicethrowers for n=1,2,3,4... dice. You will see the distribution of the means take on more and more of a bell shape. But fully normal it becomes only when n approaches infinity (and then it will be a quite spiked bell of course :)) So, to be clear: the CLT talks about behavior when n approaches infinity. The CLT can be used approximately before that, but it's a very bad approximation when n=1.