Mathematical puzzle Puns

I was looking at this old puzzle from an Ancient Egyptian papyrus known as the Rhind Mathematical Papyrus.

It said:

" 100 loaves of bread must be divided among five workers.

Each worker in line must get more than the previous: the same amount more in each case (an arithmetical progression).

And the first two workers shall get seven times less than the three others.

How many loaves (including fractions of a loaf!) does each worker get?"

Now, to solve it:

Let's say the middle person who gets the most loaves gets w loaves, and d is the difference between them, we thus have:

w-2d, w-d, w, w+d, w+2d.

We know that w = 20 since it's the average.

Now, to plug it into an equation:

7*[(20-2d) + (20-d)] = 20 + (20+d) + (20+2d).

d = 55/6 in this case, and w is the average.

We already know that the middle worker will get a perfect average. But why? I know that if they were spread out equally, it's 20 loaves each. But why is it that the middle worker always gets a perfect average? Why then is w always the average?

Thanks.

No, they do not. Such sound-alike statements as found in the media on almost a daily basis are pure pseudo-reference, like those images of shiny golden bitcoins so popular with art directors. We need to help journalists with this. They need a journalistically short and direct distillation of what miners do instead of the opaque mantra they blankly recite today -- something that will tickle readers and journalists alike into learning more. I suggest something like:

>Miners convert blocks of transaction data into a series of letters and digits unique to those transactions and with the required number of leading zeros as their Proof of Work.

I think a good rule would be to limit the statement to one sentence of no more than thirty words and with no word over three syllables and no more than one or two of those, as per the above example.

A futile effort? Absolutely. But let history show that we tried.

Edit:

>Miners convert blocks of transaction data into a series of letters and digits unique to those transactions and with the required number of leading zeros as their Proof of Work.

New improved suggestion:

>Using a program published in 2001 by the NSA, miners race to create numeric digests of bitcoin transaction-blocks that meet the system's evolving Proof of Work requirement.

Might be able to reduce the sentence by a word by dropping the from the NSA -- Washington D.C. denizens often do that with gov't acronyms. Thus, Using a program published in 2001 by NSA . . .

I originally made a typo! I changed it:

If 1 = 1, 2 = 5, 3 = 28, 4 = 164, then 5 = ?

The answer has to be a number from 1-400, since you have to go to the page with your number to check your answer.

I'm trying to teach mathematical reasoning through stories about the puzzles the main character solves in his adventures. This is supposed to be accessible to teenagers and fun for adults. Any feedback would be much appreciated :)

https://docs.google.com/document/d/1UcFUhzfD27rAp34hnXO-gnSCWm5L--BALcG1rNIInX4/edit?usp=sharing

Dear past CS 2100 students,

I am currently taking CS 2100 and I am wondering if anyone had a copy of this book (in the title) I could borrow for the semester? Or, lmk if u wanna be study buds and share the book with me :). I really appreciate it.

This is a little number puzzle I came up with on short notice for a session today. It turned out quite well so I figured I should share it. My group of two players figured it out in about 30 or 40 minutes, which felt like the right amount of time. They went down a couple wrong paths with it but didn't ever really get stuck. As a math puzzle, it will be easiest for players who have some kind of math background, but anyone with a middle-school education should probably be familiar with the concepts involved. The setup I used involved the door to an abandoned pirate lair but really it could slot in most anywhere you need a single-room puzzle encounter.

There are three statues (arranged in a circle, or however else you like): an eagle, a rabbit, and a boar. Each statue is carved with a huge gaping mouth, and on inspection the tongue can move slightly if weight is put on it. Nearby (in an offering bowl, or wherever else is convenient), there is a pile of 100 copper pieces (or gold pieces, if you like giving out big piles of money). A wall, plaque, door, map, etc. nearby has the following clue on it:

> The eagle is proud, and will not divide his meal with anyone.

> The rabbit feeds all his children, twice as many each generation.

> The boar needs a meal of a meal, a pile of food upon itself.

> Leave no food to waste.

The basic premise, which my genre-savvy players figured out pretty much immediately:

>!You need to put the coins into the statues mouths. Each statue wants a certain amount of coins, and there can't be any left over.!<

The solution:

>!The eagle will accept any prime number of coins, i.e. 2, 3, 5, 7, 11, 13, etc.!<

>!The rabbit will accept any power of two, e.g. 1, 2, 4, 8, 16, 32, 64. You could also reasonably read the clue as needing to feed all the rabbits in every generation, in which case the total should be one less than a power of two, e.g. 1, 3, 7, 15, 31, 63.!<

>!The boar will accept any square number of coins, i.e. 1, 4, 9, 16, 25, etc.!<

>!Any of several solutions that meets those criteria and leaves no coins left over is acceptable. I had figured out at least one beforehand, just to make sure it was possible. Possible solutions include (59, 16, 25) or (3, 16, 81) or (43, 8, 49). If your players go for the other interpretation of the rabbit, possible answers include (5, 31, 64) or (29, 7, 64) or (89, 7, 4).!<

The puzzle is in figuring out the patterns. From there, it's pretty easy to f

My province (Ontario) is doing online school for the third time and I want something to occupy me. To elaborate, I want some more recreational math puzzles, not puzzles that revolve around some math, like sudoku. An example of one is this:

A frog wants to cross a river and there are 9 lily pads between it and the other side. The frog will jump any amount of spaces forward with the limit being the end. (At the beginning it could jump from 1-10 spaces.) What is the average amount of jumps the frog will take in order to get to the other side?

I undertook this project and found it very interesting (so interesting, in fact, that I may make a separate post about it). Even references to places where I could find some would be great.

Thx

Does anyone smile inside whenever anyone describes bitcoin mining as "solving complex mathematical puzzles"? I see it described that way a lot. But isn't bitcoin mining just random guessing and checking at a massive scale? It just amuses me that my favorite grade-school method of solving math problems (guess and check) is now being described as "complex mathematical puzzle solution" for a 1 trillion dollar asset class

Hey Guys! I have a question that i hope i can ask here. I wasnt able to find a proper answer to this online. Miners (PoS) generally speaking create a hash from all the transactions in a possible block and the Parent Hash. Then the mathematical puzzle is to finde a random number (nonce) that will result in a certain hash.

For Bitcoin this was easy to understand. Here (depending on the difficulty) the hash needs to be lower than a certain number (thus new blocks' hashes have so many beginning zeros). But here my question: what exactly are ethereum miners looking for. When looking at blocks on etherscan.io i was not able to find a pattern. Is it also some kind of "find a hash lower than 0x9..."? If anyone can help me out with the mining process in ethereum 1.0, that would be awesome.

Thank You!

I have spent lots of time trying to solve this puzzle myself but unfortunately without success. The letters are to find the coordinates for a Geocaching puzzle but for the purpose of solving this puzzle they can be ignored totaly. I hope someone can help.

https://preview.redd.it/v5pjgm6du9261.png?width=1105&format=png&auto=webp&s=1f382fd28bb3d7439d2290396abe250b614cdb03

Stay Safe

I am pretty sure it was American and produced last decennium. I've searched Google and it literally is at the tip of my tongue. I am praying the following rings a bell with someone.

I only remember vague parts of this movie or series, so I am just going to jot down the random things of the plot I remember:

• the detective somehow finds out that the missing people all played some weird phone puzzle game
• he tracked payments from the missing girl's bank account and finds out something about her mother sending her money
• the missing girl had been living with acquaintances for a while. He visits that home
• he also visits someone who lives on a boat
• he somehow finds out about an old mansion and finds someone who is addicted to the game in the attic.
• this person has scribbled weird mathematic equations on the wall
• this person jumps out of the window (I think)
• apparently this game has many levels which get harder and harder and drives people crazy
• there is money or a prize involved if the levels get solved
• he finds a community of weird people who are into this game

I really don't know why I remember so little from this story. I hope someone can help me! <3

I present to you two rooms based on mathematical problems that make for interesting puzzles for players to interact with. Both rooms have an out for players that don't quite get it and would rather brute force them. Their reward for executing the problems correctly is getting through the rooms with more of their resources intact.

If anyone has any ideas on some mathematical problems or decision making puzzles that might make for good dungeon rooms please comment them. I'd like to put them together into a "the Riddler meets Acererak" style dungeon.

1: Monty Hall

The party enters a room with three doors one Red, one Blue, and one Yellow. On a pedestal in the center of the room rests three keys that are color coded to each door. The pedestal bears the inscription “One key shall lead to your salvation, two lead to your doom.”

As the inscription says, one door opens to the path forward and the other two contain deadly monsters. When any key is picked up for the first time a door whose color does not match the key and that has a deadly creature behind it becomes translucent, allowing the players to see the danger beyond. The players may choose to use the key they have picked up first to unlock the corresponding door, but discerning players will place this key back on the table and choose to open the last of the three doors. This method isn’t surefire; however, it will give them the greatest chance of success.

Optionally, you may choose to make one creature or trap deadlier than the other. In which case, if the players pick up the “correct” key first the DM should reveal the deadlier of the two remaining options so that players are still rewarded if they make the wise decision to choose the final door. If the players survive their encounter, then they can open the remaining door and proceed.

2: The Josephus Problem

The party enters a room with 41 numbered seats arranged in a circle and a magically locked door which requires a password to unlock. A cryptic message is scrawled in blood across the floor that reads “the survivor knows.”

When any player takes a seat in the circle, they are given a vision. In this vision 41 knights are seated in a circle and the player represents the knight seated in the same seat they chose. The first of the knights (seat 1) slays the man to his right (seat 2), and the man to his right (seat 3) slays the man to his right (seat 4). This pattern repeats until only one knight is left alive; however, if the knight whose POV the pl