In fact, it is even 2 < n < m < 100, since the numbers are distinct.
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Ok guys, so, there’s been quite a lot of activity during the past few days (thanks @yebellz for resurrecting our old forgotten thread). If you guys don’t mind, your contributions will be appearing as Problem of the week as we used to in our main group.
The protocol there was let each one simmer for seven days before posting the next one, so they’ll be appearing in the next few weeks. You can also check out the old problems in the news section, there are quite a few interesting ones.
The Egg Hunt
In celebration for this newfound interest, I’ve put a 
hidden treasure somewhere on OGS. It could be anywhere
it could be here
(it is not though).Although you could find it by guessing where it is—and there is more than one way to get there—I’ll give you a couple of things to help you get started:
- Here are two codes: 2875*8, 313312; have at thee!
- If you’ve ever had an indestructible old brick, it might help you decode them.
- Remember, GIYF (search this if you don’t know, you’ll see why).
That’s it. Good luck!
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Ok, here’s another one (Content warning: trypophobia).
The queen bee is building a honeycomb to accommodate her larvae. She builds following the usual rules:
- Each cell is hexagon shaped;
- Each cell has to be completely surrounded by other cells;
- And she builds 3 cells around each intersection.
Image: “Honeycomb” by justus.thane is licensed under CC BY-NC-SA 2.0
However, sometimes she can make mistakes: she may put a pentagonal cell instead of a hexagonal one. This is the only kind of mistake she allows herself to make though; barring that, any botched nests would be thrown away.
Eventually, she realizes she’s finished—and in her first try!
-
How many mistakes did the queen make?
-
What is the largest number of larvae that is impossible to accommodate exactly one-to-one on each cell?
Edits for clarification:
Very important omission: Hexagons and Pentagons need not be regular
Second question: some nest sizes are impossible to build. What is the biggest one?
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So Vsotvep (or do you want this link?) asked me the other day something along the lines of “What if the evil logician is sadistic? How long can he keep Alice and Bob in, if they can still escape?”
So I figured that out.
Same scenario as before. The evil logician captures Alice and Bob and puts them in separate prison cells. He tells Alice the sum of two numbers 1 < m < n < 100 (makes no difference) and Bob the product. Each night, he comes to Alice, then Bob, asking if they know the numbers. They may pass or guess. If one guesses correctly, they will both instantly be freed. If one guesses incorrectly, they will both be stuck forever.
For the first 6 nights, both pass, and nothing happens. On the 7th night, Bob guesses correctly and both are free.
What are the numbers?
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I shared this problem with a friend and after giving the answer he said the question is flawed. To quote:
Hmm, “first summer baby” rules out twins, but how do you rule out kids born 9-12 months apart?
E.g. suppose kid B was born in September 2010 and kid C was born in July 2011. In August 2013 they both will be 2.
But I guess if information was sufficient for holmes, this dialogue did not happen during July-October when such situation can exist?
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Yes, this was also my conclusion. We know that information was sufficient for Holmes, thus we know the conversation must have been held outside of July - October.
I don’t see it as a flawed puzzle, just one where the truth is a little more obscure than apparent at first glance.
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Oh, right!
By the same logic, there was no 4th hint!
Ten days have past, and the Egg Hunt is yet to have any takers. Ironically, this kind of puzzle is meant to be discovered, not hidden forever. Something hidden forever may make a good secret (or a very good troll), but the one thing it does not make is a good game.
The main lesson I’ve learned from playing “20 questions” in these forums is that I should provide better clues.
With that in mind let’s revise those clues, shall we?
So, I guess the acronym is kind of unnecessary? To wit GIYF ain’t GIF, it ain’t Jif and it sure ain’t Giphy. GIYF simply means that Google is your friend; don’t waste the help of a good friend.
However, most speculation seems to emanate from the second clue. What is this artifact that can apparently decode those sequences? I am very aware now that not everyone here is a millennial, and my choice of a dated joke might not have been the best.
Believe it or not, this ancient tablet was once common amongst the common folk. It was a meme of the people. It has been dubbed the unbreakable and made into a picture character in the land whence it came.
I hope, with this, speculation becomes less unwieldy than before.
I believe I have once owned the object described in your second hint. Truly remarkable things they were, staying completely functional even after dropping down two flights of stairs and getting submerged in the Donau.
My trouble is using it to decode the first two number clues…
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The Traveling Surfers Problem
Samantha, Benjamin and Kevin are three very disparate friends. Sam is a sportswoman, she loves the X Games and has even won a competition or two; Ben is a conservationist, he works at a local vegetarian bakery and volunteers at the animal shelter; Kevin is the son of two farmers from the Midwest and really enjoys that traditional life, he also speaks several languages (Spanish, Russian, Chinese, Turkish… lost count).
The three of them met at college in California, where they discovered one thing they had in common: all three loved surfing.
Often times they’d go on trips together on summer vacation, ride the waves from dawn till dusk, and share their vastly diverging life experiences. They really hit off, up until graduation, when their careers and busy schedules took them to different places.
A few years afterwards, they managed to reconnect, and planned a trip to revisit their alma mater and to ride those waves together, once again, like they used to. As they sat, chilling, watching the sunset, their old friendship rekindled.
—So, what did you do last year?—Ben asked.
—I traveled abroad—Sam replied.
—Me too!—Ben and Kevin exclaimed in unison.
They laughed.
—Well, maybe we went to the same country—said Sam—. Here’s some silly trivia: I realized that the name of my country contains all the initial letters of the colors of its flag.
Kevin though about it for a second.
—That’s also true of the country I went—he concluded.
—Yeah!, same with mine—Ben remarked—. However, knowing us, we probably weren’t even in the same continent!
The three of them agreed. This was true even before knowing it.
—So, how were the waves over there?—inquired Kevin.
—Nah!—replied Ben—I didn’t actually pack my surfboard.
—Me neither!—Sam and Kevin exclaimed in unison.
They laughed.
-
Why had none of them packed their surfboards for their respective last year trips?
-
If they hadn’t been surfing, what had they been doing instead?
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Isn’t all of this mini games?it should be in the mini games thread
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It’s part of this group, and why would we suddenly start putting these puzzles (not games in my opinion) in a different thread if we already have this thread for it?
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I’m not sure if it is exactly “mini games” because it is modeled after things of a different style.
Think Project Euler but not necessarily so mathy. Think online puzzle games but not as big or sophisticated (yet 
). It is in spirit supposed to be as accessible as possible to a general audience.
Whether it should have the “General Chat” tag or the “Forum Games” tag is somewhat debatable; however, this is of a different origin than the current trend of games.
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Perhaps they simply didn’t want to pay the luggage fees?
Spoilers
I guess the only countries that fit this clue are Botswana, Kyrgystan, Switzerland? All of which are landlocked.
I have no idea how to determine this, or even say who went where, except to speculate based on their background.
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Intended for @yebellz, spoiler for everyone else, I guess.
Spoiler
Some level of speculation is acceptable, as long as it makes sense. It is OK if you’re able to say “Well, presumably, they probably were doing x, y and z.”
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Some level of speculation…
Spoilers
Kevin went to Switzerland to visit the family of his fiance Steve. Although he came from a family with traditional, conservative views, he is happy and loved since his parents have wholeheartedly accepted him and his partner. He enjoyed adding the Swiss-dialects of French and German into his growing language repertoire. This trip mostly confined Kevin to the urban landscape of Geneva, where Steve’s family all live, but he hopes that in future trips, he will get to experience more of the beautiful Swiss countryside, which would fondly remind him so much of his rural roots.
Ben took a job in the financial sector and quickly rose through the ranks in a private equity firm. He went to Kyrgystan for business to negotiate with a forestry company located there. While this career path seems at odds with his conservationist and social activist background, he views it as a means to an end, both in terms of making as much money as possible in order to donate to causes that he cares about, and to shape the business practices of the companies that he works with toward more environmentally friendly directions.
Sam went to medical school after college and has trained to become a doctor. Although she emerged as a promising candidate, giving her the ability to choose among career paths at various high-paying and prestigious medical institutions, she has not focused on pursuing money, and anyways already comes from a very wealthy family. In between periods of residency at a teaching hospital that humbly serves a needy part of her home city of New York, she volunteers with Médecins Sans Frontières, and spent last summer in Botswana addressing the public health emergency caused by a tropical disease epidemic. As she dedicates her life to helping those most in need, her past X-Games glory fades as a distant memory of a more hedonistic youth.
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You got me, man! You know I love a good story.
Of course, (spoiler)
I had them do much more touristy things,but this be canon now.
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I like how their continued backstories effectively are forms of “although this is their background, they are now doing something different”
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Obviously, if someone does not guess exactly the solution that I wrote down, they must have gotten the logic puzzle wrong.
Of course, that was fully intentional, and I just wanted to take the speculation to the extreme by picking paths that would not have been suggested.
These characters were very loosely based, in various parts and pieces, on people that I have known from high school and college. Although, people may have a particular background, where they go in life can be incredibly surprising.
However, I messed up a bit with contradicting that Ben “works a local vegetarian bakery”. Let’s pretend that is just a passion project that he does on the side, or what we he did back during his college days as side income while studying.
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