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# Morningstar

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## Posts posted by Morningstar

1. ### Making Ice

Freeze one tray fully, then take all the ice cubes out except two, one in one corner and one in the opposite corner. Put two cubes in each tray in the same pattern, fill them all with water, and balance them on top of each other using the already-frozen cubes as supports.

2. ### Whether to switch

I wrote a quick Java program to generate the total amount gained from switching or not over 100,000 trials with an envelope value of 1,000. Although the random number generator isn't entirely random, I thought it might help nonetheless.

import java.util.Random;

public class ProblemTest {

public static void main(String[] args) {

Random gen = new Random();
System.out.println(100000000);
long total = 0;
int otherenv = 0;
for (int i = 0; i < 100000; i++) {
otherenv = gen.nextInt(2);
if (otherenv == 0) {
total += 500;
} else if (otherenv == 1) {
total += 2000;
}
}
System.out.println(total);
System.out.println((double) 100000000 / total);

}

}

Total from not switching: 100,000,000.

Total from switching: 124,854,500.
The ratio: 0.8009322851799494.
3. ### Tial by liars

If I'm reading the problem correctly, Alex is being charged with a specific robbery. Even if he has committed robberies in the past, he's still innocent if he did not commit this one.

Ian's and Jamie's statements are inherently contradictory. I believe therefore that one of them must be true. If Ian's statement is true, and Alex has committed more than 12 robberies, then he has committed at least one, which makes Davie's statement true as well. Since only one of the statements can be true, both Davie and Ian are lying. Jamie is telling the truth, and Alex is innocent.

4. ### Is the name of this island Oahu? That depends on who is asking.

Say Sam is type A. That would mean that the answer to the question "Are they both type B?" would be true. However, that means that Sam is type B, which is a contradiction since he was assumed to be type A. Therefore, Sam is type B.

Since Sam is type B, the answer to the question "Are they both type B?" would be false. In order for this to be false, one of them has to be type A, and since Sam was assumed to be type B, Janet has to be type A.

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5. ### Going through the tetrahedron

If I understand this correctly, the solution is as follows:

The orientation of the hologram doesn't matter. Your tetrahedron is oriented the same as the hologram, and its edges are infinitesimally shorter than those of the hologram. Every point in your tetrahedron will pass through at least one point in the hologram.

6. ### Chess problems

Didn't know that, thanks.

7. ### Mission to Mars!

I take it in such a way that 4 ships are connected to a 5th ship from 4 sides to give it the energy all the trip ,i.e. only the central ship will be functioning and the others adhering to it are as energy suppliers only.

Yes...thats right...Thanks

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time. All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction. For the second quarter, Spaceship #2; and so on until landing on Mars. Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

Dear wolfgang, the solution that you consider correct suffers from two problems: 1) It violates common understanding of thermodynamics and 2) even if we allow such violation, it does not satisfy the conditions in your original post. Here is why

From your original post, each ship needs to make constant trajectory corrections since "without fuel the spaceship will miss its direction". The solution that you accept states that 4 space-ships can "piggy-back" on the course correction ability of 1 ships. That is, the ships would be tethered in such a way that adjusting the course of 1 ship would alter the course of the whole.

Of course, a simple understanding of physics would indicate that we don't really save any fuel if we allow 1 ship to change the course for all 5. If a single ships needs to make a minor course correction, it would need to provide enough thrust (energy) to move its mass however much required. If a single ship is tethered to 4 other ships, Newton's equation (F=ma) implies that the navigating ship would need 5 times the energy to alter the current course. So, in reality, tethering 5 ships together would make the single navigating ship burn fuel 5 times as fast as it changes course.

That said, even if we allow such violation, how do you suppose to get the ships home. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Even allowing for the thermodynamics violation, all your 5 ships would end up on Mars with 1 tank left, which is only good enough for 1/4 of the way back to the moon base.

While I understand that lateral and out-of-box thinking are valued around here, in general such solutions have to be internally consistent (and avoid violating explicit conditions set forth in the original post). Also, in this forum, we obey the law of thermodynamics.

I don't see how that helps. Since the controlling ship still needs 5x the amount of fuel to go the same distance, it would only get 1/8 of the way before having to turn back.

8. ### Chess problems

I was thinking that it might be interesting if there was a section in the forum for chess problems, maybe with support for chessboard pics. Not sure how difficult it would be but it might be cool.

9. ### Give a monkey enough rope

If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ... Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

So the rope has legs and plays footbal?! And monkey's mother is a male?! And age is money?!Was it Google translation? I guess, it'll be awhile before computers can understand and translate natural language.Although it's worth noting that about the only bit translated correctly, is that very thing, which I misunderstood. The translation states, the weight of the rope together with the weight is 1.5 times the weight of the monkey, as the problem statement intended. Whereas I understood it as half weight of the monkey.
I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

The rope ran over a pulley on one end of a monkey on the other end ves.Dva remaining ravnovesii.Ves war was 4 oz / football, and at the age of monkeys and apes mother was four goda.Ves monkey was a lot of pounds, as a mother monkey was years, and the weight of weight and the weight of the rope together were half as much as the weight of the monkeys.

Weight weight weight exceeded rope as many pounds as a monkey years old when his mother was twice as old as the monkey monkey brother was a mother monkey was twice as old as his brother is a monkey, the monkey when the brother is three times as old as the mother monkey When she was a monkey three times as old as the monkey in paragraph 1.

Mother was twice as old as the monkey monkey monkey When the mother was half as old as the monkey will be when the monkey is three times as old as the mother monkey was when the mother monkey is three times as old as the monkey in paragraph 1.

Maternal age exceeded the age of his brother monkeys monkeys in the same amount as age exceeded the age of his brother monkeys monkeys.

What was the length of the rope?

10. ### The birthday coincidence

Are we using your age as shown on your profile page (72)?

No, Sherlock, but great investigative reporting!
Oh that makes things different. In that case I think there are several solutions.

Actually, what was the point in saying that it is twice your age? All it tells us is that the sum is even, but we already know this as any 3 numbers formed from the prime factorisation of 2450 sum to be even.

Your statement is correct.

Your question is valid.

But since you don't yet have a unique answer, it's your question to answer.

Btw, no offense intended by the Sherlock comment.

None taken.

11. ### The birthday coincidence

Are we using your age as shown on your profile page (72)?

12. ### How Many Primes?

None. They are all divisible by 3 and 9 (the sum of 1 through 9 is 45 and is divisible by 3 and 9)

Wow. That was fast. Good job!

13. ### How Many Primes?

Just a quick math problem that shouldn't take too long.

The digits 0-9 can be arranged into 3,628,800 distinct 10-digit numbers (including a leading 0). Of these, how many are prime?

14. ### How can you weigh a living fish?

The problem says that we can't take the fish out of the aquarium, or put in new water. However, it doesn't say we can't take the water out of the aquarium. So, remove all the water, quickly weigh the fish, and then put back the water. Simple!

15. ### BRIAN DENNIS: WARM-UP

Sorry I haven't really been active, I haven't had a lot of time to post what with school and stuff, but I'll check in periodically and if I have anything important to say I'll say it.

16. ### BRIAN DENNIS: WARM-UP

Howard is another maid, right? If so, she's probably just nervous about being interrogated. Just my input.

17. ### BRIAN DENNIS: WARM-UP

What is the taser actually for?

Could we tase Morningstar as a demonstration?

Discreetly of course we don't want to be accused of unethically torturing the unresponsive or invalidate intended lie detector results.

Edit: If the butler sees explain that this is what we do to those who we have failed the lie detector test and hopefully we will be more inclined to get the truth out of him.

Edit: Still need to know if the body has tan lines indicating that a watch was worn. Need to ask coroner maybe?

18. ### BRIAN DENNIS: WARM-UP

What is the taser actually for?

19. ### BRIAN DENNIS: WARM-UP

How do we know that the watch belonged to the murderer? It's pretty hard for your watch to fall off without you noticing, so it was probably put there deliberately. Also, where in the suit was the watch found? I.e. in the wrist part, just loose inside, etc.

20. ### BRIAN DENNIS: WARM-UP

Sorry, it just makes it easier for me to tell what's what when I'm looking through the posts.

21. ### BRIAN DENNIS: WARM-UP

Some of the answers that look like lie detector results aren't in blue. Is it just my browser?

Edit: Also, where is the trophy room relative to where the body was found?

22. ### BRIAN DENNIS: WARM-UP

Hey guys, looks like we're back at it again. Awesome start to a mystery as always, Cav.

23. ### The Witch's Epigraph, Chapter Two: The Helix and the Rose

Hello? Anyone there?

Also, 200th thread post!

24. ### Can you decipher this?

Looks like nobody's replied... any hints?

25. ### The Witch's Epigraph, Chapter Two: The Helix and the Rose

Where is everybody?

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