1,874 reputation
21133
bio website
location Palo Alto, CA
age 24
visits member for 3 years, 9 months
seen 2 hours ago

Jan
28
asked Why should we care about groups at all?
Jan
15
awarded  Good Answer
Jan
12
accepted A distance preserving operator that's not linear?
Jan
10
revised A distance preserving operator that's not linear?
added 79 characters in body
Jan
10
asked A distance preserving operator that's not linear?
Jan
10
accepted Why do we define functions over $open$ subsets of $\mathbb{R}^n$?
Jan
6
asked Why do we define functions over $open$ subsets of $\mathbb{R}^n$?
Dec
31
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 $9 \times n$?
Dec
25
awarded  Nice Question
Dec
25
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.
Dec
23
revised Two seemingly unrelated puzzles have very similar solutions; what's the connection?
added 134 characters in body
Dec
23
revised Two seemingly unrelated puzzles have very similar solutions; what's the connection?
deleted 53 characters in body
Dec
22
revised When the roulette has hit 5 reds why shouldn't I bet to black?
deleted 646 characters in body
Dec
22
answered When the roulette has hit 5 reds why shouldn't I bet to black?
Dec
22
comment Two seemingly unrelated puzzles have very similar solutions; what's the connection?
Your updated solution definitely works!
Dec
21
revised Two seemingly unrelated puzzles have very similar solutions; what's the connection?
added 272 characters in body
Dec
21
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.
Dec
21
comment Two seemingly unrelated puzzles have very similar solutions; what's the connection?
Some great insights here! I definitely agree with you that both graphs and permutations come up. In fact, I would argue that these insights are vital for solving the puzzles in the first place. However, I disagree with you on a few points. In particular, I don't think that (1) a boolean array of size m is constant memory, or that (2) removing a[1] makes problem 6b look like the locker puzzle (since the cycle in problem 6b could start anywhere in the array, while you're always stuck in a cycle for the locker puzzle).
Dec
21
comment Two seemingly unrelated puzzles have very similar solutions; what's the connection?
In the case where only one entry is duplicated, I imagine you could just sum the array values and subtract $2 + 3 + \ldots + n$ to find the duplicate entry :) OK, so technically that requires storing an integer on the order of n^2 (which might not be allowed), but I'm going to sweep that one under the rug because on any "real" computer that would be the sensible thing to do...
Dec
21
revised Two seemingly unrelated puzzles have very similar solutions; what's the connection?
added 6 characters in body; added 6 characters in body