Search found 2084 matches

by jaap
Wed Jun 12, 2019 8:20 am UTC
Forum: Mathematics
Topic: "tricky" factoring problem
Replies: 20
Views: 4597

Re: "tricky" factoring problem

Thanks, I've never really seen a problem of finding solutions in integers worked out before. FYI, if you apply the same method to the circle a^2+b^2=z^2 with known point (0,z,z) then you get the well known parametrization of Pythagorean triples (u^2-v^2, 2uv, u^2+v^2). This is a lot less messy than...
by jaap
Wed Jun 12, 2019 5:12 am UTC
Forum: Mathematics
Topic: "tricky" factoring problem
Replies: 20
Views: 4597

Re: "tricky" factoring problem

How did you find these, and does this include all solutions? Yes, it should include all solutions. From ab=cd we know that c=at, d=b/t for some rational factor t. Substitute in a+b=c-d to get a+b=at-b/t. This is a quadratic in t which has determinant a^2+6ab+b^2. We want this determinant to be perf...
by jaap
Tue Jun 11, 2019 8:55 pm UTC
Forum: Mathematics
Topic: "tricky" factoring problem
Replies: 20
Views: 4597

Re: "tricky" factoring problem

I have found the parametrization to these pairs of quadratics. The expessions a = -(3k-1)(5k+3) b = 2(k+2)(k-5) c = -2(k+2)(5k+3) d = (k-5)*(3k-1) satisfy ab=cd and a+b=c-d. As mentioned before, they can be multiplied by the same scaling factor, which I haven't explicitly included. For example: For ...
by jaap
Wed Jan 23, 2019 3:41 pm UTC
Forum: Mathematics
Topic: Fractions help.
Replies: 13
Views: 3732

Re: Fractions help.

Like visualizing 4/3 ÷ 3/2 I could do the problem but but I'm having trouble understanding it in reference to a number line. I've seen a few videos but the all use examples were the denominators are the same. You can make the denominators the same. A fraction stays the same value if you multiply de...
by jaap
Sat Jan 05, 2019 8:04 am UTC
Forum: Science
Topic: Science fleeting thoughts
Replies: 445
Views: 65418

Re: Science fleeting thoughts

(I am the last poster in the place I might have otherwise put this, so choosing here, in lieu of a completely new thread.) While we're waiting for additional post-Ultima Thule data being assembled (and the alien structures being paintshopped out, for public consumption), don't ignore the Japanese m...
by jaap
Mon Dec 17, 2018 7:23 pm UTC
Forum: Mathematics
Topic: Average Difference between 2 Dice
Replies: 15
Views: 6053

Re: Average Difference between 2 Dice

DavidSh wrote:jaap, you might want to check your work.

Thanks. I had n-1 instead of n+1 in my formula. Fixed it now.
by jaap
Mon Dec 17, 2018 4:54 pm UTC
Forum: Mathematics
Topic: Average Difference between 2 Dice
Replies: 15
Views: 6053

Re: Average Difference between 2 Dice

Suppose we have two n-sided dice, throw them both and take the highest of the two values. Then there is only 1 way to score 1. There are 3 ways to score 2 (1&2, 2&2, 2&1). There are 5 ways to score 3 (1&3, 2&3, 3&3, 3&2, 3&1). ... There are 2n-1 ways to score n (n wit...
by jaap
Mon Nov 26, 2018 10:06 am UTC
Forum: Logic Puzzles
Topic: Car
Replies: 3
Views: 2376

Re: Car

This puzzle has been discussed here before too, as part of the Crossing the desert thread.
by jaap
Mon Nov 26, 2018 9:56 am UTC
Forum: Logic Puzzles
Topic: Tube
Replies: 2
Views: 2073

Re: Tube

This puzzle has been asked and answered here before:
Ants on a stick
Colliding balls
by jaap
Fri Nov 02, 2018 7:04 am UTC
Forum: Logic Puzzles
Topic: Power
Replies: 2
Views: 2674

Re: Power

by jaap
Sun Oct 14, 2018 5:50 am UTC
Forum: Language/Linguistics
Topic: Language fleeting thoughts
Replies: 169
Views: 55143

Re: Language fleeting thoughts

Isogram
"Iso" means same, so shouldn't a word with all different letters be called something like "heterogram"?
by jaap
Wed Oct 10, 2018 6:41 am UTC
Forum: Language/Linguistics
Topic: Language fleeting thoughts
Replies: 169
Views: 55143

Re: Language fleeting thoughts

Eebster the Great wrote:Huh, I was talking about an old SNL Weekend Update.

That's the number bleen, which is totally different from bleem.
by jaap
Mon Oct 08, 2018 4:38 pm UTC
Forum: Language/Linguistics
Topic: Language fleeting thoughts
Replies: 169
Views: 55143

Re: Language fleeting thoughts

"if you say a word over and over, it starts to lose all meaning" Semantic satiation The mouthmand tongue feel like they're doing far more repreparation betwixt the 4 and 3 than between any of the others (understandable, F( eye fvvv )F( ore )->??->Th( r eee )T( ooo ) W (o' n ), with handy ...
by jaap
Fri Aug 31, 2018 8:51 am UTC
Forum: Logic Puzzles
Topic: Train station Puzzle Interview Question
Replies: 3
Views: 4366

Re: Train station Puzzle Interview Question

It's easy once you see it.

Spoiler:
His wife is obviously also home twenty minutes early.
This means she saved 10 minutes drive both ways to/from the station.
So she met him when she had still 10 minutes to go to the station, i.e. at 5:50pm.
He was walking from 5 till 5:50, so 50 minutes.
by jaap
Thu Aug 23, 2018 6:22 am UTC
Forum: Science
Topic: Science fleeting thoughts
Replies: 445
Views: 65418

Re: Science fleeting thoughts

Millisecond-precision timing is very impressive, and this type of thing is also necessary for throwing accurately at long distances. It is something we as humans seem to be almost uniquely good at. Humans are also very good at recognising and following patterns. I reckon that by getting a regular s...
by jaap
Mon Aug 20, 2018 11:25 am UTC
Forum: Mathematics
Topic: Cross-continuousness in higher dimensions,
Replies: 4
Views: 3427

Re: Cross-continuousness in higher dimensions,

Interesting thoughts. Just a quick quibble: ... and a stellation of a cube is just an octahedron, ... No, the octahedron is the dual of the cube. The cube, does not have any stellations : There are no stellations of the cube, because non-adjacent faces are parallel and thus cannot be extended to mee...
by jaap
Tue Jul 24, 2018 6:40 am UTC
Forum: Logic Puzzles
Topic: Tower of Hanoi Variant
Replies: 2
Views: 3157

Re: Tower of Hanoi Variant

There's a very detailed book "The Tower of Hanoi - Myths and Maths" from 2013 which has a whole chapter devoted to this. The four-peg version is also called Reve's Puzzle, given that name by H.E. Dudeney who was the first to write about this generalization in his 1908 Canterbury Puzzles. T...
by jaap
Thu Jun 21, 2018 3:55 pm UTC
Forum: Mathematics
Topic: Repetitive Coin Flip Probability
Replies: 16
Views: 7172

Re: Repetitive Coin Flip Probability

Seems like that kind of bias would have to be in the method of flipping rather than the coin itself. Quite so. Here's a demonstration of tossing a coin ten times in a row, getting heads each time. (For full disclosure: that is me, and it took me only about 7 or 8 takes. Sorry, I couldn't resist pos...
by jaap
Wed May 30, 2018 9:46 am UTC
Forum: Science
Topic: How much is 1e340 j of energy?
Replies: 19
Views: 5886

Re: How much is 1e340 j of energy?

What I was thinking is that there are some very large numbers that are useful, or at least used, in various types of mathematical explorations, ponderings or theories, perhaps used in things like cryptography (eg: very large primes) or other esoteric fields, even if its just exploring the nature of...
by jaap
Thu Feb 01, 2018 6:48 am UTC
Forum: Logic Puzzles
Topic: Rubrics Cube of Doom
Replies: 3
Views: 5133

Re: Rubrics Cube of Doom

I plan on painting over the squares of a rubrics cube It's called a Rubik's Cube, named after its inventor Ernö Rubik. Such maze cubes have been designed before. The standard maze cube design was made by Christoph Lohe, and he explains the reasoning behind it here: The Maze Cube You can buy sticker...
by jaap
Tue Jan 02, 2018 7:32 am UTC
Forum: Language/Linguistics
Topic: Is this logical statement true or false?
Replies: 15
Views: 8340

Re: Is this logical statement true or false?

[...] or that it does have meaning, and it is simply false, since there are no colorless green ideas, and therefore there can't be any sleeping, furiously or otherwise. In mathematical logic such a statement would be considered true. Non-existent objects have any property you can name because to pr...
by jaap
Fri Nov 24, 2017 9:55 am UTC
Forum: Fictional Science
Topic: How do you define..."you"?: Question about Infinite Universe
Replies: 22
Views: 8323

Re: How do you define..."you"?: Question about Infinite Universe

andykhang wrote:The alternate self idea? That's there is infinite version of you when you have infinite universe?

Are you talking about a multiverse (i.e. parallel universes) rather than a single infinitely large universe?
by jaap
Tue Nov 21, 2017 7:11 pm UTC
Forum: Mathematics
Topic: periodicity in LCGs
Replies: 2
Views: 3331

Re: periodicity in LCGs

You have X_{t+1} = (aX_t + c) mod 2^k You can simply look at it mod 2^1: X_{t+1} = (aX_t + c) mod 2 The resulting lowest bit of X_{t+1} does not depend on any of the higher bits of X_t, only on the lowest bit. Therefore, this reduced PRNG essentially has an internal state consists only of a single b...
by jaap
Fri Nov 17, 2017 11:12 am UTC
Forum: Mathematics
Topic: Maximizing 2 Variables
Replies: 19
Views: 6150

Re: Maximizing 2 Variables

Eebster the Great wrote:Again, you are maximizing the objective function, not "two variables". You can certainly maximize a function of multiple variables (if it has a maximum).

I'm not disagreeing, just explaining why you need such a function and giving a simple example.
by jaap
Fri Nov 17, 2017 9:50 am UTC
Forum: Mathematics
Topic: Assassin Problem over the Internet
Replies: 40
Views: 10655

Re: Assassin Problem over the Internet

Hmm, watching the videos, I don't like the solutions presented. The originating person's proposal is, with the extraneous stuff removed: 1. Number all the people 1-8. 2. Get cards numbered 1-8, in order. Cycle the deck (move top card to bottom) a random number of times. 3. Give the first ca...
by jaap
Fri Nov 17, 2017 9:16 am UTC
Forum: Mathematics
Topic: Maximizing 2 Variables
Replies: 19
Views: 6150

Re: Maximizing 2 Variables

Yeah, with x(t) and y(t) plotted on an x-y plane, maximizing x and y at the same time means having a cusp that "points" toward the top-right. cusp.png Such a cusp is not a general feature of parametric plots, and it's irrelevant (to the general case) that if your graph is just a line segm...
by jaap
Thu Sep 07, 2017 1:13 pm UTC
Forum: News & Articles
Topic: Bedfordshire Professor Claims Voynich Breakthrough
Replies: 15
Views: 14262

Re: Bedfordshire Professor Claims Voynich Breakthrough

**BUMP**

Another reasonably convincing interpretation:
https://www.the-tls.co.uk/articles/publ ... -solution/
by jaap
Wed Sep 06, 2017 5:55 am UTC
Forum: Logic Puzzles
Topic: 538 hats riddle
Replies: 20
Views: 9138

Re: 538 hats riddle

With 7 people you can use two rules. Rule one - If you see four people with the same color, then you must guess that you have the opposite color. Win - 70/128 Lose - 42/128 Rule two - If you see six people with the same color, then you must guess that you have the opposite color Win - 14/128 Lose -...
by jaap
Mon Sep 04, 2017 3:14 pm UTC
Forum: Logic Puzzles
Topic: 538 hats riddle
Replies: 20
Views: 9138

Re: 538 hats riddle

It is not stated clearly in the question, but I assume that each hat's colour is chosen independently, 50:50 either colour. What you say is true if you make a fixed choice beforehand about who is going make a guess. However, you don't have to do that. For example, consider the smaller version of the...
by jaap
Sat Sep 02, 2017 1:59 pm UTC
Forum: Language/Linguistics
Topic: Miscellaneous language questions
Replies: 590
Views: 127395

Re: Miscellaneous language questions

Maybe at some point the y spelling had dots added because as I wrote before the letter y is not used much normally. In cursive handwriting the ij is essentially identical to y apart from the dots, and it is very hard to resist the urge to automatically add them. That is really interesting. Is this ...
by jaap
Sat Sep 02, 2017 11:53 am UTC
Forum: Language/Linguistics
Topic: Miscellaneous language questions
Replies: 590
Views: 127395

Re: Miscellaneous language questions

Non-English 26ers include Dutch (Ij directly replacing Y, it seems, a detail to which I would clearly defer to any Dutch forumite who cared to comment) I'm Dutch, so let me wade in here about the Dutch "IJ". It represents a vowel sound, one of the many diphthongs spoken Dutch has. It is n...
by jaap
Fri Sep 01, 2017 2:27 pm UTC
Forum: Mathematics
Topic: Possible "Spot it!"-like decks
Replies: 30
Views: 9476

Re: Possible "Spot it!"-like decks

See I thought that when you made cards like these it was what he was asking about. I thought these worked, Meets all his conditions. 1376524 1745632 1234567 1472635 1563472 1625743 All your cards have the same symbols. We don't care about their order on each card, so every pair of cards in your set...
by jaap
Thu Aug 31, 2017 9:40 am UTC
Forum: Language/Linguistics
Topic: Miscellaneous language questions
Replies: 590
Views: 127395

Re: Miscellaneous language questions

Non-English 26ers include Dutch (Ij directly replacing Y, it seems, a detail to which I would clearly defer to any Dutch forumite who cared to comment) I'm Dutch, so let me wade in here about the Dutch "IJ". It represents a vowel sound, one of the many diphthongs spoken Dutch has. It is n...
by jaap
Wed Jul 26, 2017 12:06 pm UTC
Forum: Mathematics
Topic: Determining line of sight over time
Replies: 30
Views: 7890

Re: Determining line of sight over time

By the way, having the observers moving instead of stationary does not change the difficulty of this question. Are you dropping the implicit assumption that the objects in the space are stationary? I guess so, because I never really thought of the objects as stationary. *since the line end points r...
by jaap
Wed Jul 26, 2017 5:21 am UTC
Forum: Mathematics
Topic: Determining line of sight over time
Replies: 30
Views: 7890

Re: Determining line of sight over time

Sure. I'm trying to understand the point? Do you think her/his problem is solvable? The OP is not clear: If both points are stationary is it trivial to determine whether or not they can see each other. However, both points are moving. As you said, and I agree, that part is still essentially trivial...
by jaap
Tue Jul 25, 2017 2:40 pm UTC
Forum: Mathematics
Topic: Determining line of sight over time
Replies: 30
Views: 7890

Re: Determining line of sight over time

There are two points in a space. The space is filled with objects. If both points are stationary is it trivial to determine whether or not they can see each other. However, both points are moving. Luckily, they are moving in straight lines with a constant speed. How would I go about determining at ...
by jaap
Mon Jul 24, 2017 11:57 am UTC
Forum: Logic Puzzles
Topic: Arithmetic puzzle
Replies: 5
Views: 7679

Re: Arithmetic puzzle

It is not possible.

For n>1 we have:
log n! < log nn = n log n < n2

So n! always has fewer than n2 digits (except for 1! and 0!).
by jaap
Fri Jul 21, 2017 12:28 pm UTC
Forum: Logic Puzzles
Topic: Isosceles triangles and circles : puzzle connection
Replies: 15
Views: 7534

Re: Isosceles triangles and circles : puzzle connection

Read what was written in the picture : "At right you have samples of isosceles triangles connecting three circles" Is there any precision about right triangle or not? no. So triangles could be right or not. Just watch carefully my examples : you have right triangles and not right triangle...
by jaap
Sun Jul 16, 2017 5:27 pm UTC
Forum: Movies and TV Shows
Topic: Doctor Whom
Replies: 4990
Views: 771361

Re: Doctor Whom

charliepanayi wrote:We have a female Doctor

Jodie Whittaker
by jaap
Fri Jul 07, 2017 7:52 am UTC
Forum: Language/Linguistics
Topic: How to write in plain language
Replies: 32
Views: 12120

Re: How to write in plain language

Are you getting that 20 words/sentence average from your personal digital copy? I admit that is an awful lot. On the other hand, by Shane Snow's calculations , Hemingway's books have an overall Flesch-Kincaid reading level of 4, and reading ease of a startling 95. So clearly it matters which metric...

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