Miscellaneous trivia, riddles, puzzles and other games


#1

Timing is everything

For anyone who’s been lingering about these forums during the past few months, you know the drill: this is the part where I announce some annual event in the hopes that it’ll survive the turn of 2020. But please bear with me a little longer, because this is not it. Believe me, I have tried, and it’s a pain in the neck…

… (also, I keep my alternative accounts safely tucked under a low profile :slight_smile:)


What is this about, then?

Besides Go, I like playing games, solving puzzles, and that kind of stuff. I remember the Mathematics Room on KGS, where they would post a few interesting problems every now and then. I’m not sure if it is still active, but I don’t aim to make a copycat of that, rather, something more varied and accessible. I love the idea of online puzzles of the likes of notpron, even though I could not create (or solve) such a thing.

So, I recycled this group, where (for now) I intend to be posting games and puzzles somewhat regularly. I’m very interested to know if you have challenges of your own, for discussion on this thread, all in good fun.

To whet your appetite, I’ll leave you with two opening trivia:

  1. What is the oldest internet go server?
  2. What is the oldest OGS account?

If you answer one of these, I’ll invite you to our first mini-tournament. Just because.


EDIT: Please, as a general guideline, don’t spoil the answers to these puzzles. You can send Private Messages to the puzzle creator if you want to check if your answer is correct

You can also use the following template:

<details>
<summary>SPOILER</summary>
This text is hidden
</details>

Which looks like this:

SPOILER This text is hidden

#2

Hi guys,

New problem of the week is out, give it a try :slight_smile:

Problem #8: A science riddle

(by iridium)

When she is 18
and the cat is 91
How old is the mouse?


Please remember not to spoil the answer, you can send a Private Message to the puzzle creator instead. Discussion is otherwise encouraged.


#4
Summary

The mouse is 18, you said that at the start


#5

Oh, the detail tag did work for you? I couldn’t make it work for myself. (EDIT: it works now, I must have made some sort of mistake)

I’m afraid that is not the answer,

because she is not the mouse.

#6

New problem, not as cryptic as the last one :wink:

Hope you people like a bit of geometry.


Problem #9: Circles and segments

(by iridium)

If the radius of a circle is 2 units
and the radii are two sides of a right angled triangle
What is the area of the segment created
by the hypotenuse and the segment arc?


Bonus round:

What is the arc length of the segment?


Please remember not to spoil the answer (read the first post), you can send a Private Message to the puzzle creator instead. Discussion is otherwise encouraged.


#7

One of our newest members came up with this puzzle invloving some “epistemic trickery”.

Can you tell what do you know that he knows that you know? :thinking:


Problem #10: Some Sum Puzzle

(by Vsotvep)

A teacher is testing his best students Albert, Bernard and Cheryl with a little game. He glued a piece of paper with a number written on it on each of their foreheads and told them that one of their numbers is the sum of the other two numbers, and that each of the numbers are between 1 and 5. The students can’t see their own foreheads, but they can see each other.

After the explanation the teacher asks Albert if he knows what number he has, to which Albert responds “No sir, but I know that Bernard also doesn’t know it”. The teacher then turns to Cheryl and asks whether she has the largest number or not. Cheryl, smart as she is, thought for a few seconds and declared “I didn’t know it before Albert answered your question, but I do know it now whether I’m the largest or not!” and then she proceeded to write the answer on a piece of paper which she showed only to the teacher.

  • What did Cheryl write on the piece of paper?


Bonus round:

During lunch break Diana, friend of Bernard’s, told him that she’d been eavesdropping the conversation, but that there was something still bugging her. “What was going on?” she asked. "Well," Bernard responded, “if you had lined us up in alphabetic order, you could have moved one of us towards the front of the line and get the numbers in ascending order”. Somehow, Diana was satisfied with this answer.

  • What were the numbers on their foreheads?


Please remember not to spoil the answer (read the first post), you can send a Private Message to the puzzle creator instead. Discussion is otherwise encouraged.


#8

Problem 8

solution

The wording is a bit awkward, since the pronoun “she” is used ambiguously, but that particular word is crucial since I think the answer relies on the specific letters of the words corresponding to chemical elements. The key hint is calling it a science riddle.

“she” = S (sulfur, 16) + He (helium, 2) = 18
“cat” = C (carbon, 6) + At (Astatine, 85) = 91

“mouse” = Mo (molybdenum, 42) + U (uranium, 92) + Se (selenium, 34) = 168


#9

Problem 9

solution

This one isn’t really a riddle, but rather just a simple grade school math problem.

The wording is a bit clumsy, but I am assuming that you are essentially just asking for the difference between the area of a circle and that of a square inscribed inside of it, divided by four (since we are just looking at a quarter of the picture, where it is just a right triangle inside of a quarter of a circle).

The area of the quarter circle is simply pi, and the area of the triangle is 2, so the area of the section between the hypotenuse and the arc is pi minus two.

The arc length is pi (a quarter of the circumference).


#10

Problem 10

Solution

This type of problem just requires working out all of the possibilities and eliminating the cases that are excluded.

Out of all of the ways to assign numbers, there are only eight scenarios that Albert could have seen that would have left uncertainty to him about what number was on his forehead:

  1. B = 1, C = 2 (A = 1 or 3), B must be uncertain
  2. B = 2, C = 1 (A = 1 or 3)
  3. B = 1, C = 3 (A = 2 or 4)
  4. B = 3, C = 1 (A = 2 or 4), B must be uncertain
  5. B = 1, C = 4 (A = 3 or 5)
  6. B = 4, C = 1 (A = 3 or 5)
  7. B = 2, C = 3 (A = 1 or 5)
  8. B = 3, C = 2 (A = 1 or 5)

Essentially, there are four observable pairs {(1,2), (1,3), (1,4), (2,3)} that would leave uncertainty. Only in scenarios 1 and 4 would Albert know with certainty that Bernard does not initially know (note that Albert’s statement immediately reveals to Bernard what his number was). In the other scenarios, it is possible that Bernard observes a pair that makes his number certain.

Expanding these scenarios, we have four total cases left:

  1. B = 1, A = 1, C = 2, (excluded, since C would have known she had 2)
  2. B = 1, A = 3, C = 2 (Cheryl was initially uncertain, could have been 4)
  3. B = 3, A = 2, C = 1 (Cheryl was initially uncertain, could have been 5)
  4. B = 3, A = 4, C = 1, (excluded, since C would have known she had 1)

However, cases 1 and 4 are excluded since Cheryl would have known before Albert spoke. In the two remaining cases, Cheryl does not have the largest number, so she wrote “no” on the paper.

The information in the bonus question reduces the possibility to only case 3:
A = 2, B = 3, C = 1
since in case 2, it is not possible to move just one person to the front to get the numbers in ascending order.

Another puzzle

The “blue-eyed islanders” puzzle is really neat

xkcd presentation: https://xkcd.com/blue_eyes.html
solution: https://xkcd.com/solution.html

Terence Tao wrote a detailed blog post: https://terrytao.wordpress.com/2011/04/07/the-blue-eyed-islanders-puzzle-repost/
Further discussion: https://terrytao.wordpress.com/2011/05/19/epistemic-logic-temporal-epistemic-logic-and-the-blue-eyed-islander-puzzle-lower-bound/


#11

I present to you another epistemic puzzle, my personal favourite:

Problem #12: A Rational Problem


Albert and Bernard are being tested by their teacher once more. He gives them both a little note with a number on it, and he tells them both numbers are different from each other and of the following form for n and k natural numbers larger than 0:

1/2n + 1/(2k+1)×2n


Then the following conversation happens:

Teacher: "Who of you has the smallest number?"
Albert: "I don't know."
Bernard: "I also don't know."
Albert: "I still have no clue."
Bernard: "No, nothing for me either."
Teacher: "You two can keep going like this for a long time, but you will never find the answer like this."
Albert: "Ah, that's very interesting information, yet still I don't know if I'm the smallest."
Bernard: "Neither do I."
Teacher: "Again, continuing like this will not lead any of you two to know their number."
Albert: "That is truly remarkable, but I do not know if I have the smallest number."
Bernard: "Nor do I."
Albert: "Ah! But now I suddenly know who is smaller!"
Bernard: "Fantastic, then I know both of our numbers!"

Which numbers are written on Albert’s and Bernard’s notes?