Some of the problems posed by Brilliant are correctly stated but interpreted incorrectly in terms of the supplied solutions. For example, the problem with the heatloss from penquins assembled in a large huddle, asked if there were any penquins that lost heat at a different rate than others? And I would assume that answer would be given in clear, consise terms. However, the 'solution' seemed to hinge on the fact that in a huddle, every member radiates in a more-or-less 360 deg horizontal plane. Given the picture of the 'huddle' that was presented in the problem statement, it is clear to any 'moderately intelligent' individual that this is not a homogeneous huddle. It has internal members, and 'edge' members. Clearly the ' internal' ones radiate less 'net' heat than the 'edge' members. Why your 'solution' dwelled on the fact that they all radiate indentically, completed missed the correct approach which observes that they are NOT all equivalent. Try to be more careful with your assumptions and you will more respect.