Curiosity On Rails

The following question was dubbed the hardest logic puzzle, published in 1996, written by the renowned founder of theoretical computer science, Raymond Smullyan. One of the reasons I took it up in this blog was because after reading many articles explaining the answer, they were more of a reverse engineered solution and none of them, in my opinion,worked up-to the solution such that I could solve any question of this form posed(reason why I was not content with such explanations). Here's the Hardest Logic Puzzle Ever  : Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for “yes” and “no”...

Is it possible that the dice (singular form: die) that we get with our monopoly game/other games is not within the rules of it being called an unbiased die ? Maybe not. Hypothesis : Die is unbiased To test this hypothesis, the first question that arises (due to sheer lassitude) is - what will be the minimum number of tests/throws to get enough data of statistical importance? According to Pearson's ${\chi }^2$ test   , the rule of thumb is to atleast have 5 times the total sample space of a single die. The die has 6 sides, so we need atleast 30 tests . To get more significant results, this will be repeated 3 times to give better results. In the first test, we threw the die  40 times  and its values are: 6,4,3,1,2,5,3,1,4,2,5,3,1,1,3,2,5,3,1,2,3,5,4,2,3,6,1,4,2,3,4,2,5,6,2,3,1,2,6,4 : $sum=127$ Throw methodology: All throws were made with the right hand pivoted at a point and arc length of the throw was marked such that the same distance was covere...