If this is your first time here, read the rules below! There are no excuses if you break them.
Current PuzzlesStart off with something relatively simple...The Inheritance(RSP: Inheritance)Problem Statement: In ancient times, a father with two sons must decide who amongst them will gain his entire fortune. He decides to have both his sons race on their horses to a city some distance away. The father, not being one for normality, adds a significant twist to the rules: the
slowest horse, the one who arrives to the city last, wins. Arrival at the city is of course still necessary for claiming the prize, so off the two sons go.
After spending a few days making sure to travel as little as possible each day, they come across a wanderer, who asks the sons why they're moving so slowly. After explaining their situation, the wanderer gives the sons some helpful advice on their race. After this talk, the two sons take off on their horses, trying to reach the city before the other.
What advice did the wanderer give?
Read the twist to the rules again. Carefully.
Since the arrival condition only applies to the horses, and not the sons themselves, they switch horses and thus are now trying to get their brother's horse to lose.
You are on the infamous game show
Let's Make a Deal, a contestant in the infamous "Three Doors" game, in which one door hides a car (which you'll gladly accept), while the other two doors each hide a goat (which you are not obligated to accept). The rules of the game are simple:
- Pick any one of the three doors.
- Monty Hall, our fabulous host, opens one of the doors hiding a goat. He will never open the door you picked.
- You are asked if you would like to stick with your original pick, or if you'd rather switch to the other unopened one.
- Monty opens the door that is your current selection. You either win a car, or a goat.
Should you switch doors or hold steadfast? What is the chance that you'll win the car if you stay? What about if you switch?
If you've never seen this problem before, and it took you all of 2 seconds to come up with an answer, you're probably wrong.
You should switch. You have a 1/3 chance of winning if you stay, and a 2/3 chance if you switch.
One way of explaining this is as follows: when you make your first choice. You have a 1/3 chance of picking the car door, and a 2/3 chance of not picking the car door.
════┼════┼════┼════
| | |
1/3 ------
2/3When Monty reveals one of the two unpicked doors, the chance of that door holding the car is 0. But, that group of two doors still has a 2/3 chance of containing the car. So, the last door in the group now bears all that probability.
════┼════┼════g════
| | |
1/3 | 0
2/3Thus switching is a better choice.
More explanation can be found at
this helpful pageThere are none! Congratulations, you're seeing this OP at the beginning of the thread's life!
RulesHello, and welcome to the Puzzle Your Brain™ thread, where the love of solving puzzles and exercising our thinking muscles in general guides our time here. The general format is to provide puzzles (in this OP) for people to work on, and to hopefully also allow discussion of whatever puzzle strikes your fancy. Please read the rest of these rules before starting.
Posting Solutions and AnswersAs you converse with others on this thread, you may wish to post your answer and/or solution. If you are to do so, please put the answer or solution in a spoiler. You should title the spoiler (using [spoiler=TITLE] syntax) with the Recommended Spoiler Prefix (RSP), listed directly underneath each puzzle in the OP. If you're discussing a puzzle not in the OP or one that is in the OP and is somehow missing its RSP, you should use something suitably descriptive. (For reference, the RSP is usually the most important couple of words in the puzzle title.)
If the puzzle comes with a solution or answer already provided, you do not need to post the answer again, just state that you have solved it. Your solutions, if they differ from the given one, may be posted under spoiler anyway.
Posting HintsIf you want to provide hints to others in the midst of some puzzle solving, then of course you may. If your hint makes figuring out the answer stupidly easy, you should probably spoiler it (complete with RSP. See above section). If you are in doubt as to whether or not you should spoiler a hint,
spoiler it.
If somebody (especially me!
) asks you to spoiler an unspoilered hint, you probably should.
Non-OP PuzzlesFirst, consider if your puzzle may not be better handled by an existing help thread:
If you feel the puzzle you have on mind can be discussed here, feel free to do so! Just keep in mind these few tips:
- Unless the puzzle is common or simple enough that it would take relatively no effort to solve/find the solution, you should probably withhold the answer. Can't make it too easy for everyone.
- Puzzles that are particularly perplexing may end up being an OP puzzle come next OP change. This should be taken as a compliment
- Do not badger people to solve your puzzle above all others. We'll get to it in time.
Submitting PuzzlesIf you wish to submit a puzzle for consideration, just request it here! If you're particularly paranoid about people working on it before it's an OP puzzle, you can currently PM it to me.
In general, your puzzle should be:
- Interesting.
- Moderately Complex (takes more than a few minutes to solve).
- Bonus: Problems you came across in your daily activities are likely far more fun than those you can find by googling "brainteasers".
For the time being only, submission of typical problems is acceptable. This is just so we get them out of the way for more fun and unique puzzles in the future. You only need to mention common puzzles by their name to submit them. (Because they are common, it won't take me much time to search for them.
)
TangentsIf, while solving any of the puzzles here, you find yourself asking more questions ("What if there were two car prizes in Monty Hall?" "Why is this guaranteed true?" and so on),
that is totally awesome! The whole point of this thread is to have fun problems to (sometimes frustratingly) mull over. Going on tangents means you're mind is wandering (and wondering), and that means you're engaged in the puzzle. Make us engaged too, and share!
If you solve any of these puzzles:- P versus NP
- Hodge Conjecture
- Riemann Hypothesis
- Yang–Mills existence and mass gap
- Navier–Stokes existence and smoothness
- Birch and Swinnerton-Dyer conjecture
Please, do not post your answer here. You are hereby instructed to notify your preferred mathematics journal with your findings.
CivilityI shouldn't have to put this here, but I'll do so anyway:
- Treat people kindly.
- Don't mock people for not understanding puzzle or their solutions.
- Et Cetera.
You'll be reported for such gross acts of incivility.
Final ThoughtsThe ultimate point of this thread is to be a place for people who enjoy chewing on problems of various complexities, who are in the unfortunate situation of having no such problems. So, as long as you keep with this theme, you're doing fine. I expect the rules and nature of this thread to morph over time as you guys take this starting post and run with it. I will of course guide the discussion, but I won't control it with an iron fist.
Allons-y!
Author
Topic: Puzzle Your Brain — Let's Make a Deal-ightful Debut (Read 640 times)