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Activity for Peter Taylor
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #296688 |
Maybe generalise a bit to `[hidden-message]`? (more) |
— | about 3 hours ago |
| Comment | Post #296684 |
The first two puzzles would be good candidates for a `[3d-packing]` tag as a subtag of `[packing]`, but `[3d]` by itself seems too vague to me. The third puzzle is not a 3D puzzle at all: the setting is 2D non-Euclidean geometry. (more) |
— | about 4 hours ago |
| Edit | Post #296675 | Initial revision | — | 2 days ago |
| Answer | — |
A: Closed loop on an octahedron Solution Process An easy observation is that every triangle has an edge which the line does not pass through, so we're really tiling with four diamonds: I placed the red diamond arbitrarily due to symmetry. Since the top half of the red diamond couldn't be part of a cycle of length 4 around... (more) |
— | 2 days ago |
| Comment | Post #296672 |
This is very close to [the problem](https://en.wikipedia.org/wiki/Icosian_game) which is the origin of the name "Hamiltonian cycle". (more) |
— | 2 days ago |
| Edit | Post #296668 | Initial revision | — | 3 days ago |
| Answer | — |
A: Closed loop on a side length 2 cube Solution Process I start with a fairly symmetric placement which doesn't meet the constraints and make simple modifications until it does. We have two "single" and two "double" tiles per side. We can place them to leave four vertices of the cube clear: Now place the double tiles in the rem... (more) |
— | 3 days ago |
| Edit | Post #296592 | Initial revision | — | 24 days ago |
| Answer | — |
A: Place an X into seven of the squares Simple strategy A greedy strategy works. Place X in squares 1, 2. (1, 2) excludes 3. Available: (4, 5, 6, 7, 8, 9, 10, 11, 12, 13). Place X in square 4. (1, 4) excludes 7. (2, 4) excludes 6. Available: (5, 8, 9, 10, 11, 12, 13). Place X in square 5. (1, 5) excludes 9. (2, 5) excludes 8. (... (more) |
— | 24 days ago |
| Edit | Post #296570 | Initial revision | — | 29 days ago |
| Answer | — |
A: Rearrange to make 5 fives My solution All five lines positioned so that their centres are on top of each other and rotated by different multiples of 72 degrees ExplanationThis works by using the Roman numeral V for five. There are ten "simple" Vs formed by each half-line and its clockwise neighbour, and I would argue als... (more) |
— | 29 days ago |
| Comment | Post #296532 |
I can see how to make it appear considerably more than 5 times, along the lines of the "how many triangles are there in this picture" puzzles. (more) |
— | about 1 month ago |
| Edit | Post #296486 | Initial revision | — | about 1 month ago |
| Answer | — |
A: How much money was in the bag? Reasoning and solutionThere must be at least 7 1-dollar bills, at least 8 2-dollar bills, and at least 11 5-dollar bills. That constrains 26 of the 26 bills, so the total is 7 + 16 + 55 = 78 dollars. Alternative, in case it's a trick questionAt least 78 dollars. The question doesn't say anything ... (more) |
— | about 1 month ago |
| Edit | Post #296485 | Initial revision | — | about 1 month ago |
| Answer | — |
A: Draw the boundaries of the eight dominoes ```txt +---+---+---+---+ | | | 0 0 1 3 | + + | | | 1 1 0 3 | + + | | | 2 3 3 2 | + + | | | 3 2 2 1 | +---+---+---+---+ ``` Step 1 The `3` in the bottom-left must be with one... (more) |
— | about 1 month ago |
| Comment | Post #295850 |
[My automated solver in Python](https://gist.github.com/pjt33/390b953efa6af4bc251f1238867c6674) finds only the solution already given in will's answer, modulo symmetries of the square. (more) |
— | about 1 month ago |
| Edit | Post #296471 | Initial revision | — | about 1 month ago |
| Answer | — |
A: Find the shortest possible string containing all permutations of 1, 2, 3 Proposed solution123121321 for 9 symbols. Reasoning The first three symbols should be a permutation because otherwise we can trim the first symbol without losing any permutation. Without loss of generality we can start with `123`. Given a prefix, call a one-symbol continuation of it "good" if i... (more) |
— | about 1 month ago |
| Edit | Post #296470 | Initial revision | — | about 1 month ago |
| Answer | — |
A: Using the given numbers, make an expression whose value is 639 A solution using fewer than 6 of the numbers $$\left(75 + \frac{50}{25}\right)\times 7 + 100 = 639$$ (more) |
— | about 1 month ago |
| Comment | Post #296456 |
The edges of $K_5$ can be partitioned into two copies of $C_5$; making one cycle monochromatic red and the other monochromatic black generalises this solution. Now, if three edges from $A$ are red then the edges which join their other ends must be black, forming a black triangle, so every vertex ... (more) |
— | about 2 months ago |
| Edit | Post #296462 |
Post edited: |
— | about 2 months ago |
| Edit | Post #296462 | Initial revision | — | about 2 months ago |
| Answer | — |
A: Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left? Solution- Reasoning Two of the same sign collapse to +; two different signs collapse to -. This is isomorphic to the multiplication rules, so the entire question is isomorphic to: > A large whiteboard has 2014 (+1) and 2015 (−1) written on it. You are allowed to replace two numbers by their pro... (more) |
— | about 2 months ago |
| Edit | Post #296461 | Initial revision | — | about 2 months ago |
| Answer | — |
A: Fill the 4x4 grid with numbers to make eight arithmetic progressions Solution ```txt 27 34 41 48 19 31 43 55 11 28 45 62 3 25 47 69 ``` Reasoning Filling in the first column as an arithmetic progression and then the rows as arithmetic progressions we get ```txt 27 27+b 27+2b 27+3b 27+a 27+a+c 27+a+2c 27+a+3c 27+2a 27+2a+d 27+2... (more) |
— | about 2 months ago |
| Edit | Post #296451 | Initial revision | — | about 2 months ago |
| Answer | — |
A: What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another? Answer4 amazons. Achieving the claimed result ```txt .A... ....A ..... A.... ...A. ``` The claimed result is optimal If we have five amazons then every rank and file must have one. Consider the central file. Up to symmetry there are three squares where we can place an amazon, and each of t... (more) |
— | about 2 months ago |
| Comment | Post #296402 |
In computer game design, particularly multiplayer games with an economic system which depends on time spent playing the game, this kind of task is known as a "time sink". (more) |
— | about 2 months ago |
| Edit | Post #296291 |
Post edited: |
— | 3 months ago |
| Edit | Post #296291 | Initial revision | — | 3 months ago |
| Answer | — |
A: Find three distinct integers such that all pairwise sums are powers of 2. If we supposeA+B=2, A+C=4, B+C=8 thenGaussian elimination gives A=-1, B=3, C=5. The only restriction(other than the obvious observation that the sums must also be distinct) is that the sums must all be even. Perhaps the intention was that people would assume that any solution can be divided do... (more) |
— | 3 months ago |
| Comment | Post #296200 |
Fair enough. I've added both and a bit more explanation. (more) |
— | 4 months ago |
| Edit | Post #296200 |
Post edited: Apparently Markdown link syntax doesn't work inside <summary> blocks |
— | 4 months ago |
| Edit | Post #296200 |
Post edited: Link Sprague-Grundy and explain N- and P-positions |
— | 4 months ago |
| Edit | Post #296200 | Initial revision | — | 4 months ago |
| Answer | — |
A: Delta and Epsilon play a game with marbles Solution Yes, by Sprague-Grundy. The same comment as I made on the related question applies. Answer to what I suppose to be the intended question $146$ is an N-position (the next player to move wins), so Delta can win. Details The P-positions (previous player wins) are $5k$ and $5k+2... (more) |
— | 4 months ago |
| Comment | Post #296179 |
The pedantic answer is "Yes", and if a proof is required then it expands to "Yes, by Sprague-Grundy". From your acceptance of Olin's answer, I suspect that the question should really be "Which player has a winning strategy, and what is it?" (more) |
— | 4 months ago |
| Edit | Post #292532 | Initial revision | — | about 2 years ago |
| Answer | — |
A: What could be a believable reason for technologically advanced underground people to not notice the end of surface war for hundreds of years? I've read one novel with a similar setting where the answer was: a small number in the government know the truth, but they intentionally deceive everyone else in order to retain power. Anyone who wants to go outside is given a protective suit and sent into exile, but the suit is sabotaged and kil... (more) |
— | about 2 years ago |
| Comment | Post #291871 |
I was thinking that the line between games and sports is a tricky one, and since you've brought it up... What about pub games? Darts, pool, bat and trap, etc. require some physical ability, but don't involve much physical exercise. (more) |
— | about 2 years ago |
| Comment | Post #291658 |
What asymmetry do you claim exists between that scenario and a crime being committed by a high-ranking police officer? (more) |
— | over 2 years ago |
| Comment | Post #291657 |
As illustrated by my argument with Lundin in comments on their answer, the question of the "unique... role in society" of police is complicated by the fact that the organisations called "police forces" have different roles in different societies (and some societies have many different "police" fo... (more) |
— | over 2 years ago |
| Comment | Post #291658 |
Crime can be investigated by judges rather than police: that's essentially the Napoleonic system. Criminals can be arrested by the army or by the general public, as happened before professional police forces. (more) |
— | over 2 years ago |
| Comment | Post #291658 |
You need fair courts with minimal corruption to execute the principle that everyone is equal before the law, but the existence of fair courts is not predicated on the existence of a professional police force. There is also an element of defining what "police" means: not all police forces have his... (more) |
— | over 2 years ago |
| Comment | Post #291658 |
Very little of this answer is about the police, who are separate from the courts; organised police forces predate modern democracy, rather than following it; class, wealth and gender still affect the chances of winning in democracies; advocates to plead someone else's case go back well before the... (more) |
— | over 2 years ago |
| Comment | Post #291191 |
The answer to this will depend on where you live, because differing local regulations and economies will result in differing available options. Where I live, no-one would need to ask because there are specific collection points at the doors of all the supermarkets. (more) |
— | over 2 years ago |
| Edit | Post #291147 |
Post edited: This must have been a typo because otherwise it's not an example of the title |
— | over 2 years ago |
| Suggested Edit | Post #291147 |
Suggested edit: This must have been a typo because otherwise it's not an example of the title (more) |
helpful | over 2 years ago |