Miscellaneous trivia, riddles, puzzles and other games

I’m stumped by this one:

Holmes once had a visit from an old acquaintance whom I had never met before. I found them chatting freely in a way he seldom did with me as I came in to offer them some tea.

“And how are your children?” Holmes was asking. “You have three, if I remember rightly, although I must admit I don’t quite recall their ages.”

“You always enjoyed deduction, didn’t you, old chap?” his acquaintance replied. “What if I told you that the product of their ages was 40?”

“That’s not quite enough information for me to deduce their ages,” said Holmes.

“Alright, well I shall add that the sum of their ages is the number of years we’ve known each other.”

Holmes considered this. “I’ll still need a tad more.”

“Finally, the youngest was our first summer baby, born in July.”

“Ah, I see.”

Holmes suddenly turned to me. “Why don’t you tell this gentleman the ages of his children, then, Watson?”

I balked. “But I don’t know how long you’ve known each other!”

“That doesn’t matter, Watson! You now have enough information to deduce it.”

And indeed I did. How old are the three children?

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Do you want this published in the group news? We haven’t updated in a long time

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Sure, I don’t mind that you do. I’m not the author of this riddle, of course, and I don’t know the answer.

I love it! It reminds me of Conway’s bus wizards.

Last night I sat behind two wizards, Azemelius and Bartholomew, on a bus. I heard this conversation:

Azemelius: I have a positive integer number of children, whose ages are positive integers. The product of their ages is my own age, and the sum of their ages is the number on this bus.

Bartholomew (looking at the number of the bus): Perhaps if you told me your age and how many children you had, I could work out their ages?

Azemelius: No, you could not.

Bartholomew: Aha! At last I know how old you are! (Bartholomew had been trying to find Azemelius’s age for a long time.)

What is the number of the bus?

(shamelessly copied from this site)

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I still can’t get over that he passed away. RIP

Here’s one:

Alice and Bob, two perfect logicians, are captured by an evil logician, who believes that the world should be rid of all those who are not perfect logicians.

He puts them in seperate prison cells, with no communication to one another. However, he offers a way to escape.

He gives Alice the sum of two distinct positive integers greater than 2 and less than 100, and Bob the product of them.

He explains:

“I gave Alice the sum, and Bob the product, of two distinct positive integers strictly between 2 and 100. Every night, at 8:00, I will come to each of you, first Alice, then Bob, and ask if you know what the two numbers are. You may pass, or guess. If one of you guesses correctly, you will both be freed. If one of you guesses incorrectly, you will both be stuck here forever! Good luck!”

The first night, Alice passes, and then Bob passes. Bob wasn’t sure if Alice would be able to figure it out, but the next night, Alice does get it right and both are freed.

Bob says, “So the sum was odd, right?” Alice says yes.

Assuming Alice and Bob would escape at the first possible opportunity, and do not take any chances, what are the numbers? What would they be if the sum was even (2 solutions)?

(edited for clarification)

(another edit: I forgot to state that Bob wasn’t sure whether Alice would know. That’s quite an important point, otherwise there would be 2 more solutions for both the odd riddle and the even riddle.)

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For clarification, is it

  • 2 < n,m < 100

or

  • 2 ≤ n,m ≤ 100 ?

It is 2 < n,m < 100.

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 :old_key::moneybag:hidden treasure:moneybag::old_key: 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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@Vsotvep, mad scientist and time wizard, gets it

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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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