Elliott
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 Jan29 comment Why should we care about groups at all? Great example, though I wish they would emphasize this aspect more in quantum mechanics classes! Jan29 revised Why should we care about groups at all? added 20 characters in body Jan29 revised Why should we care about groups at all? deleted 54 characters in body; added 93 characters in body Jan28 asked Why should we care about groups at all? Jan15 awarded Good Answer Jan12 accepted A distance preserving operator that's not linear? Jan10 revised A distance preserving operator that's not linear? added 79 characters in body Jan10 asked A distance preserving operator that's not linear? Jan10 accepted Why do we define functions over $open$ subsets of $\mathbb{R}^n$? Jan6 asked Why do we define functions over $open$ subsets of $\mathbb{R}^n$? Dec31 comment What makes $9$ special? Here's something else to try: write a number $n$ such that the digits, read left to right, are increasing (e.g. 12345 or 13579). What is the sum of the digits of $9 \times n$? Dec25 awarded Nice Question Dec25 comment Two seemingly unrelated puzzles have very similar solutions; what's the connection? Thanks, this is really interesting! Here's a sketch of my solution; please let me know if there's a more elegant approach. Lemma: if the first $k$ cards don't contain card $1$, then every one of those $k$ cards will reach the top at some point (induction on $k$). Now suppose card $1$ is in position $k+1$. One of the first $k$ cards must be $>k$. After that card reaches the top (guaranteed by the Lemma), the next step will send that card below card $1$, and card $1$ will get closer to the top. Since $k$ was arbitrary, this process will continue until card $1$ is at the top. Dec23 revised Two seemingly unrelated puzzles have very similar solutions; what's the connection? added 134 characters in body Dec23 revised Two seemingly unrelated puzzles have very similar solutions; what's the connection? deleted 53 characters in body Dec22 revised When the roulette has hit 5 reds why shouldn't I bet to black? deleted 646 characters in body Dec22 answered When the roulette has hit 5 reds why shouldn't I bet to black? Dec22 comment Two seemingly unrelated puzzles have very similar solutions; what's the connection? Your updated solution definitely works! Dec21 revised Two seemingly unrelated puzzles have very similar solutions; what's the connection? added 272 characters in body Dec21 comment Two seemingly unrelated puzzles have very similar solutions; what's the connection? Finally, if there's truly no deep connection, I think that "why do they have this common subproblem and where else does this subproblem come up" would still be an interesting question.