In fact, it is even 2 < n < m < 100, since the numbers are distinct.
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!
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?
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?
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?
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.
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?
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…
@Vsotvep, mad scientist and time wizard, gets it