Timeline for Puzzle in Martin Gardner book [closed]
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2011 at 4:47 | history | closed |
Gerry Myerson Douglas Zare Bruce Westbury Gerald Edgar Qiaochu Yuan |
off topic | |
| Jul 14, 2011 at 19:01 | vote | accept | columbus | ||
| Jul 14, 2011 at 11:35 | answer | added | Johan Wästlund | timeline score: 1 | |
| Jul 14, 2011 at 11:21 | answer | added | maproom | timeline score: 1 | |
| Jul 14, 2011 at 5:11 | comment | added | Douglas Zare | A nontrivial variation is that you choose what fraction of your bankroll to bet on whether the next card is red or black. As long as you bet on the favored side (if any), and you choose to bet everything if only one color is left in the deck, then your expected bankroll does not depend on your other choices. Also, there is a strategy so that you end up with the same amount regardless of the ordering. | |
| Jul 14, 2011 at 5:01 | comment | added | Gerry Myerson | The consensus seems to be that the problem has no offical name and there is no deep insight to be had, so I have voted to close. | |
| Jul 14, 2011 at 1:57 | comment | added | S. Carnahan♦ | Now that we've dispensed with the deep insight of logarithmic random walks, we are left with the question of an official name. I think this question may find a happier home elsewhere on the internet, e.g., one of the sites listed in the FAQ. | |
| Jul 14, 2011 at 1:51 | comment | added | Gerhard Paseman | Andreas is right. However, I also think a better hint would be that multiplication is both commutative and associative. And make for a lousier puzzle name. Also, no disrespect intended, hypothetical or otherwise, for Prof. Israel. I am quite comfortable with him and his history of giving answers. Gerhard "Email Me About System Design" Paseman, 2011.07.13 | |
| Jul 14, 2011 at 1:22 | comment | added | Andreas Blass | I don't think Gerhard is objecting to the presence of Robert's comment here but to the idea of using "multiplication is commutative" as the name of the puzzle. Standard practice is that the name of a puzzle should not give away the answer. | |
| Jul 14, 2011 at 1:05 | comment | added | Todd Trimble | Gerhard, hadn't Vaughn already given the explanation before Robert Israel? Where's the harm in what Robert wrote? | |
| Jul 14, 2011 at 1:02 | comment | added | Gerhard Paseman | I don't see much of a future in Robert Israel's becoming a puzzle writer. (If he shouts spoilers out in theatres. I don't think I'll go to the movies with him either.) Gerhard "Multiplication Can Also Be Associative" Paseman, 2011.07.13 | |
| Jul 13, 2011 at 23:53 | comment | added | Andreas Blass | @Robert Israel: Maybe "multiplication is commutative" can serve as the deep insight (as well as the name). | |
| Jul 13, 2011 at 23:51 | comment | added | Andreas Blass | The question seems to presuppose that such puzzles have official names. Rather few have names at all, and I know of no way for a name to become "official". | |
| Jul 13, 2011 at 23:42 | comment | added | Robert Israel | The name I'd give it is "multiplication is commutative". | |
| Jul 13, 2011 at 23:10 | comment | added | Theo Johnson-Freyd | That said, many of Gardner's puzzles do not extend to gain deep insight, so I don't know if you'll find what you're looking for. I'm not an expert on random walks. | |
| Jul 13, 2011 at 23:05 | comment | added | Vaughn Climenhaga | So... on black cards his distance from 0 is multiplied by $\frac 12$, and on red cards it's multiplied by $\frac 32$. There are 5 of each, so after 10 steps his distance from 0 has been multiplied by $\frac {3^5}{2^{10}}$, regardless of order. There doesn't seem to be much more to it than that, or am I missing something? If you take logs, it turns back into a regular random walk, and you know how many total steps are taken each way. | |
| Jul 13, 2011 at 22:55 | comment | added | Theo Johnson-Freyd | Hi columbus: I have fixed some formatting. I think that you had intended a horizontal line between your question and the quote, but it had formatted in some strange way to make the question very large, which gave the impression of shouting. I've switched what I think is a quote from Gardner into blockquote formatting. If I have messed something up, you can revert the changes. | |
| Jul 13, 2011 at 22:53 | history | edited | Theo Johnson-Freyd | CC BY-SA 3.0 |
fixed formatting
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| Jul 13, 2011 at 22:23 | history | edited | columbus | CC BY-SA 3.0 |
deleted 8 characters in body
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| Jul 13, 2011 at 22:16 | history | asked | columbus | CC BY-SA 3.0 |