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 Feb10 awarded Citizen Patrol Nov10 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language @Qiaochu [continued] Not only was Feynman a physicist of the highest caliber, I think he had a reputation of working. Really, this problem is such a classic example it seems absurd to suppose a person like him would be unaware of it. I now think you only meant "surprised" but not "unaware", so I am on the wrong track here. Nov10 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language @Qiaochu OK, I was responding to what you said up there: "someone like Feynman would be surprised to learn that this was possible even in principle." This is something like wondering if Gauss would have been surprised at some number theory result he almost certainly played with as a child or young man. Nov9 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language @Qiaochu Do you really think Feynman would be surprised by this? This is a classic physics problem! We did this in our 12th-grade physics class (AP, non-calculus-based). Nov9 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language Your example is more about real-world limitations (physics) than "everyday language". Nov1 comment What is the remainder when $4^{44}$ is divided by 44? @Kenny Thanks for the link. Nov1 comment What is the remainder when $4^{44}$ is divided by 44? Also, moderators, what is the policy on [tastes-like-homework] questions? Nov1 comment What is the remainder when $4^{44}$ is divided by 44? @Tretwick I think Doulgas answered your question, but in an oblique way. You want to check for divisibility by 44 = 4 * 11. Four raised to any power is divisible by four, so the remaining condition is that it is also divisible by eleven. Oct19 awarded Supporter