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I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
The answer you're asking about doesn't in any way make the assumption you seem to be claiming it does.
In your "alternate" scenario:
* We find the largest single-coloured number to be read. (OK so far.)
* We count five purples in its column. (OK so far.)
* We remove that column leaving a 15x14 array. (OK so far... |
The answer you're asking about doesn't in any way make the assumption you seem to be claiming it does.
In your "alternate" scenario:
* We find the largest single-coloured number to be red. (OK so far.)
* We count five purples in its column. (OK so far.)
* We remove that column leaving a 15x14 array. (OK so far.... |
I came up with this pattern, which probably is not the desired answer but it's worth sharing anyway.
From [Rand al'Thor's answer](https://puzzling.stackexchange.com/a/109222/73282):
>! The hints are mainly about that special property of the number 4 in English, being the only one made of a number of letters equal ... |
I came up with this pattern, which probably is not the desired answer but it's worth sharing anyway.
From [Rand al'Thor's answer](https://puzzling.stackexchange.com/a/109222/73282):
>! The hints are mainly about that special property of the number 4 in English, being the only one made of a number of letters equal ... |
I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
I believe what you are asking is, "how can I go from a set of categories to drawing a grid"? I will demonstrate how to do this in two ways.
### Purpose of the logic-grid set up
First, let us establish the purpose of the logic grid. **All categories intersect, but only once**. This allows any information relating ... |
A $3 \times 3$ grid $G$ is filled with every number from the set $\{2,3,5,6,7,11,14,15,30\}$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that have a common factor greater than $1$ with $G_{ij}$. Two cells are neighbors if they are adjacent horizontally, vertical... |
Alice and Bob are planning a long car trip and need to come up with a playlist for it. For any given song, they have one of four opinions on it: "That's, like, my favorite song ever" (love), "I like that song" (like), "I'll listen to this, but you owe me" (tolerate), or "I'd rather poke my eardrums out" (hate). To bes... |
Alice and Bob are planning a long car trip and need to come up with a playlist for it. For any given song, they have one of four opinions on it: "That's, like, my favorite song ever" (love), "I like that song" (like), "I'll listen to this, but you owe me" (tolerate), or "I'd rather poke my eardrums out" (hate). To bes... |
I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
I have question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15 a... |
I have a question about the answer given to [this problem][1]. The problem is reproduced below:
> This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique.
>
> The integers 1, 2, ..., 225 are arranged in a 15×15... |
I am preparing for a competitive exam, and I am stuck on this problem which I found in one of the practice test. the image of the question in the practice test is <https://drive.google.com/file/d/1KmORwD4U7LMgOfwENfat5r7TT8Vtpkpn/view?usp=sharing>
MARRIED : 47 :: BLESS : ?
Options are:
1. 62
2. 57
3. 26
4.... |
Rule of the game-
- It's a two player game. The first move will alternate between players.
- There are N number of sticks in a table.
- both player have to take at least one and at most M sticks (2<M<=N) from the table.
- The one who takes the last stick wins.
- player cannot take p and q no of sticks where... |
Rule of the game:
- It's a two player game. Moves will alternate between players.
- There are N sticks on a table.
- On their turn, each player has to take at least one and at most M sticks (2 < M <= N) from the table.
- The player who takes the last stick wins.
- The players cannot take a number of sticks ... |
**Rules of the game:**
- It's a two player game. Moves will alternate between players.
- There are N sticks on a table.
- On their turn, each player has to take at least one and at most M sticks (2 < M <= N) from the table.
- The player who takes the last stick wins.
- The players cannot take a number of st... |
I am preparing for a competitive exam, and I am stuck on this problem which I found in one of the practice test. the image of the question in the practice test is <https://drive.google.com/file/d/1KmORwD4U7LMgOfwENfat5r7TT8Vtpkpn/view?usp=sharing>
MARRIED : 47 :: BLESS : ?
Options are:
1. 62
2. 57
3. 26
4... |
What 2-word associates with this rebus? (actually not a rebus)
[![enter image description here][1]][1]
also: What word associates with this rebus?
[![enter image description here][2]][2]
[1]: https://i.stack.imgur.com/KMKsl.png
[2]: https://i.stack.imgur.com/tp83C.png
Hints:
>! [REBUS 1] Do not l... |
A $3 \times 3$ grid $G$ is filled with every number from the set $\{2,3,5,6,7,11,14,15,30\}$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that have a common factor with $G_{ij}$ (greater than $1$). Two cells are neighbors if they are adjacent horizontally, vertic... |
I am preparing for a competitive exam, and I am stuck on this problem which I found in one of the practice test.
If found this question on [tcyonline](https://www.tcyonline.com/tests/ntse-mental-ability-mock-test). The practice test is not accessible to everyone. The name of the competitive exam is [National Talent ... |
<sub>*In the spirit of the What is a [Word™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aword+is%3Aquestion)/[Phrase™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aphrase+is%3Aquestion) series started by [JLee](https://puzzling.s... |
I am preparing for a competitive exam, and I am stuck on this problem which I found in one of the practice test.
I found this question on [tcyonline](https://www.tcyonline.com/tests/ntse-mental-ability-mock-test). The practice test is not accessible to everyone. The name of the competitive exam is [National Talent S... |
**Very Partial Answer**
I think I've got the gist of what's going on so maybe if I post what I have so far, it may inspire somebody else.
Firstly,
>! There is a strong underlying theme of chemical elements, particular chemical symbols for the elements, being used.
Post-it Note
>! The first line of the first ... |
**Very Partial Answer**
I think I've got the gist of what's going on so maybe if I post what I have so far, it may inspire somebody else.
Firstly,
>! There is a strong underlying theme of chemical elements, particular chemical symbols for the elements, being used. Moreover, I think we are looking at the first *n... |
A $3 \times 3$ grid $G$ is filled with every number from the set $\{2,3,5,6,7,11,14,15,30\}$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that have a common factor with $G_{ij}$ (greater than $1$). Two cells are neighbors if they are adjacent horizontally, vertic... |
My answer is **D** as well but I got to it slightly different way.
From right to left number of small, quarter, squares increases by 1 every step and colours get negated every step. So it looks like that (w for white and k for black background):
```
'squares': ?(**4**) - 3 - 2 - 1 - 0
'background': **K** - ... |
**Very Partial Answer**
I think I've got the gist of what's going on so maybe if I post what I have so far, it may inspire somebody else.
Firstly,
>! There is a strong underlying theme of chemical elements, particular chemical symbols for the elements, being used. Moreover, I think we are looking at the first *n... |
In the case of the four brothers at page 30, there are four brother, indistinguishable in appearance, of which
- Arthur is an accurate truth-teller,
- Bernard is an inaccurate truth-teller,
- Charles is an accurate liar,
- David is an inaccurate liar,
where "inaccurate" means that one always believes t... |
**Rules of the game:**
- It's a two player game. Moves will alternate between players.
- There are N sticks on a table.
- A value M is defined at the start of the game such that 2 < M <= N.
- On their turn, each player must take between 1 and M sticks from the table.
- A player cannot take a number of stick... |
My answer is **D** as well but I got to it slightly different way.
From right to left number of small, quarter, squares increases by 1 every step and colours get negated every step. So it looks like that (w for white and k for black background):
```
'squares': ?(**4**) - 3 - 2 - 1 - 0
'background': **K** - ... |
On page 30 of Raymond Smullyan's book _To Mock a Mockingbird_, we are told that there are four brothers, indistinguishable in appearance, of which
- Arthur is an accurate truth-teller,
- Bernard is an inaccurate truth-teller,
- Charles is an accurate liar,
- David is an inaccurate liar,
where "inaccura... |
My answer is **D** as well but I got to it slightly different way.
From right to left number of small, quarter, squares increases by 1 every step and colours get negated every step. So it looks like that (w for white and k for black background):
```
'squares': (?) 4 - 3 - 2 - 1 - 0
'background': K - W - K ... |
I'll go into a bit more detail why your proposed question works. (Personally, I think it's a very nice question, it simplifies the problem immensely).
First, let's look at accuracy. The most important point is this:
>! *Everyone* believes themselves to be accurate.
Explanation of above point:
>! An accurate... |
I'll go into a bit more detail why your proposed question works.
First, let's look at accuracy. The most important point is this:
>! *Everyone* believes themselves to be accurate.
Explanation of above point:
>! An accurate person believes themself to be accurate, correctly. They are accurate that they are a... |
In the puzzle game [Pipes][1], a space-filling [tree][2] of pipes (which may have either one, two, or three neighboring connections each, but not four) is scrambled by a series of tile rotations, and the goal is to reconstruct the solution.
**Main puzzle statement:** Is it possible for a Pipes puzzle to have multipl... |
In the puzzle game [Pipes][1], a space-filling [tree][2] of pipes (which may have either one, two, or three neighboring connections each, but not four) is scrambled by a series of tile rotations, and the goal is to reconstruct the solution. To do so, you may rotate any tile, including the "source" tile (marked with a r... |
>!Semaphore flags?
>!Semaphore flags are red and yellow and are held in one’s hands.
>!Waving the flags is the code for “Attention”, or alarm.
>!Both flags down signifies the end of a word, like how midnight is the end of the day?
>!Not sure what the ticking means, but everything else seems to fit well enou... |
Is the answer
>!Semaphore flags?
Expansion
>!Semaphore flags are red and yellow and are held in one’s hands.
>!Waving the flags is the code for “Attention”, or alarm.
>!Both flags down signifies the end of a word, like how midnight is the end of the day?
>!Not sure what the ticking means, but everythi... |
This seems a bit farfetched, but I looked though a few of the OP's historical connect walls and determined they are pretty liberal with red herrings, extra "unused matches", and stretching the idea of groups, so I am considering this at least within the realm of possibility. The key here is to note OP likes to make "at... |
I've tried to anticipate some nitpicks at the process I present below. Nitpicks are in parentheses and set off from the main method. The core of the method can be found outside the parentheses.
Set-up step:
>! Alice and Bob should construct some sort of balance. The actual form this balance takes doesn't matter, ... |
<sub>*In the spirit of the What is a [Word™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aword+is%3Aquestion)/[Phrase™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aphrase+is%3Aquestion) series started by [JLee](https://puzzling.s... |
In a country full of ancient trees known as the Republic of the Golden Bear, in what would have been the 8th month of the year, a girl was born. Victor, her Papa, went into the capital to announce her birth. Standing in the square where marriages were declared, he cleared his throat. "Ahem!" He held up a picture of her... |
Who was this girl? |
I've tried to anticipate some nitpicks at the process I present below. Nitpicks are in parentheses and set off from the main method. The core of the method can be found outside the parentheses.
Set-up step:
>! Alice and Bob should construct some sort of balance. The actual form this balance takes doesn't matter, ... |
> The prefix is a hook, but I removed one part... But it is also locked, and I forgot the key.
>
> (Just to share with you all, I am eating a salad with a raspberry vinaigrette.)
>
> The infix is my favorite numbers, which are: 1, 19, 20, 18 and 15.
>
> The suffix is like the first letter of the prefix. You jus... |
An 8x8 Sudoku where you technically only have to figure out 32 cells! <s>Twice</s> Half the cells, double the clues!
[Penpa](https://swaroopg92.github.io/penpa-edit/?m=solve&p=vVZdb9s2FH33ryAIFNsA2tGnLelhQOs0e8myNenWFUbQ0jJjC5FEVaIaV0H723v4kS2K3Q0DhsEQdXR4ee/hpe6Vuw89bwVL8AsT5jEfvzAKzBV4qbk893tdqFJk5KrfyNs+Iy+bopMbQ... |
I've tried to anticipate some nitpicks at the process I present below. Nitpicks are in parentheses and set off from the main method. The core of the method can be found outside the parentheses.
Set-up step:
>! Alice and Bob should construct some sort of balance. The actual form this balance takes doesn't matter, ... |
In autumn of the year 2003 an old man was asked about his age.
He answered: "I was born on a Sunday morning in summer and I celebrated my seventh birthday
on a Sunday morning too!"
How old was the man, when he was asked about his age in 2003? |
What is the age of the old man? |
<sub>*In the spirit of the What is a [Word™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aword+is%3Aquestion)/[Phrase™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aphrase+is%3Aquestion) series started by [JLee](https://puzzling.s... |
An 8x8 Sudoku where you technically only have to figure out 32 cells! <s>Twice</s> Half the cells, double the clues!
[Penpa Link](https://swaroopg92.github.io/penpa-edit/?m=solve&p=vVZdb9s2FH3PryBUFNsA2tGHZUt6KNA67V6ybE26DYURtLTM2EJkUZWoxlXQ/vaeSzKdFbsbBgyDIero8H4ckrpXbj90opE8wS9KuM8D/KJJaK7QT83lu9+bQpcyY1fdSt12GXtZ... |
What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit? |
In the puzzle game [Pipes][1], a space-filling [tree][2] of pipes (which may have either one, two, or three neighboring connections each, but not four) is scrambled by a series of tile rotations, and the goal is to reconstruct the solution. To do so, you may rotate any tile, including the "source" tile (marked with a r... |
If I've interpreted the rules correctly, then this should be the solution:
>! [![clones_sudoku_sol][1]][1]
**Explanation**
We start off by
>! copying over the given digits to their rotationally symmetric cell, as well as copying the thermometers for ease of solving:
>! [![clones_sudoku_1][2]][2]
Next, we
>... |
If I've interpreted the rules correctly, then this should be the solution:
>! [![clones_sudoku_sol][1]][1]
**Explanation**
We start off by
>! copying over the given digits to their rotationally symmetric cell, as well as copying the thermometers for ease of solving:
>! [![clones_sudoku_1][2]][2]
Next, we
>... |
You are given a 10-digit number: 3388766112. In each move, you can select a contiguous group of digits and increase/decrease them all by the same integer, provided that each resulting digit stays between 0 and 9 inclusive. For example, you can select the group 8766 and decrease them all by 3, resulting in 3385433112. W... |
How about this?
>! Four:
>! 3388766112
>! 3333211112 (1)
>! 2222211112 (2)
>! 2222222222 (3)
>! 0000000000 (4) |
In the figure, what is the diameter of the smallest circle assuming the two parallel lines are one unit apart?
[![enter image description here][1]][1]
Attribution: Mine, but wouldn't be too shocked if I only reinvented it.
[1]: https://i.stack.imgur.com/551tg.png |
The diameter of the smallest circle is
>! $\frac{1}{4}$
---
Let's put the figure in a Cartesian plane: (half of the figure is omitted due to symmetry)
[![enter image description here][1]][1]
Denote the radii of the four circles by $R_P = \frac12$, $R_A$, $R_B$, and $R_C$, respectively,
and let $$ R_A = ... |
The diameter of the smallest circle is
>! $\frac{1}{4}$
---
Let's put the figure in a Cartesian plane: (half of the figure is omitted due to symmetry)
[![enter image description here][1]][1]
Denote the radii of the four circles by $R_P = \frac12$, $R_A$, $R_B$, and $R_C$, respectively,
and let $$ R_A = ... |
The diameter of the smallest circle is
>! $\frac{1}{4}$
---
Let's put the figure in a Cartesian plane: (half of the figure is omitted due to symmetry)
[![enter image description here][1]][1]
Denote the radii of the four circles by $R_P = \frac12$, $R_A$, $R_B$, and $R_C$, respectively.
We see that $R_A$... |
In the figure, what is the diameter of the smallest circle assuming the two parallel lines are one unit apart?
[![enter image description here][1]][1]
Note: There is at least one elegant, geometric proof.
Attribution: Mine, but wouldn't be too shocked if I only reinvented it.
[1]: https://i.stack.imgur.co... |
<sup>*What follows here is a little Easter Egg hunt I've pulled together for you all this year. Ultimately, you need to discover **a single word of four letters in length** which will be revealed by the puzzle once all steps have been fully resolved.*</sup>
<sup>*Happy hunting, and Happy Easter!*</sup>
---
>... |
<sub>*In the spirit of the What is a [Word™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aword+is%3Aquestion)/[Phrase™](https://puzzling.stackexchange.com/search?q=%22I+call+it%22+title%3A%22what+is%22+title%3Aphrase+is%3Aquestion) series started by [JLee](https://puzzling.s... |
You are given the first 20 digits of $\pi$: 31415926535897932384. In each move, you can select a **contiguous** group of digits and increase/decrease them all by the same integer, provided that each resulting digit stays between 0 and 9 inclusive. For example you can increase the first 5 digits by 2, giving you **53637... |
You are given the first 20 digits of $\pi$: 31415926535897932384. In each move, you can select a **contiguous** group of digits and increase/decrease them all by the same integer, provided that each resulting digit stays between 0 and 9 inclusive. For example you can increase the first 5 digits by 2, giving you **53637... |
> I am uncommon,
> But a worthy goal.
> Rare but abundant
> In hill and hole.
> Who am I?
You may already know the answer, so the task is not to answer the riddle per se, but to solve the following 'What is a Word' puzzle, use the words in the puzzle to find another four word phrase (2 from each side),... |
Louis Thépault offers this puzzle in his book _Le chat à six pattes et autres casse-tête : 100 petits problèmes de mathématiques très amusants._
Four men, former classmates, met in a restaurant, each accompanied by his wife. Here’s what we know about these eight people:
1. Alexandre and his wife were born... |
A [Riley Riddle](https://puzzling.stackexchange.com/questions/62349/my-prefix-is-food-my-suffix-is-rude?noredirect=1&lq=1):
> My prefix is humble, my suffix is prime,
>
> My infix assisted a Russian in crime.
>
> I know all the secrets of this little town,
>
> And if you need me, just look around.... |
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub>
---
***After a long period of division, tends to unite; After a long period of union, tends to divide. This has been so since antiquity. - The Three Kingdoms... |
[![enter image description here][1]][1]
Text version:
| | | | |
|:---------:|:---------:|:-----------:|:-----------:|
| SNOWFLAKE | SANCTION | SHAKESPEARE | SOCCER BALL |
| COLOSSUS | GEOMETRY | DUST | SCREW NUT |
| GARDENS | AFTERNOON | HONEYC... |
When my grandfather died, he left his fine collection of coins, no more than 2500 of them, to his children, a different number to each of them, and in decreasing amounts according to their ages.
To the eldest of his children, he left one fifth of the coins, while the youngest inherited just one eleventh of them. Ga... |
When my grandfather died, he left his fine collection of coins, not more than 2500 of them, to his children, a different number to each of them, and in decreasing amounts according to their ages.
To the eldest of his children, he left one fifth of the coins, while the youngest inherited just one eleventh of them. G... |
You go in a room, the door closes. Some sign says:
>You must find a forced checkmate on the black king in two moves. The key for the Vigenere is ONLY your moves. In other words, if you played Qc3 followed by Re1 (regardless of black's moves) it would make the key Queencthreerookeone.
The chessboard:
[![enter ... |
When driving along long straight roads, this is what you would typically see:
![image][1]
<sup>Photo by <a href="https://unsplash.com/@withluke?utm_source=unsplash&utm_medium=referral&utm_content=creditCopyText">Luke Stackpoole</a> on <a href="https://unsplash.com/s/photos/path?utm_source=unsplash&utm_medium=refe... |
When driving along long straight roads, this is what you would typically see:
![image][1]
<sup>Photo by <a href="https://unsplash.com/@withluke?utm_source=unsplash&utm_medium=referral&utm_content=creditCopyText">Luke Stackpoole</a> on <a href="https://unsplash.com/s/photos/path?utm_source=unsplash&utm_medium=refe... |
Your task is to solve the Sudoku and complete the missing words in the following poem.[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/32zky.png
- Classic Sudoku: Each row column and box contains the digits 1-9.
- XV-rules: Digits separated by V must add to 5. Digits separated by X mu... |
1. A shop sells pencils in boxes of 31 and 38. What’s the highest number of pencils a person cannot buy?
In general, if the shop is selling pencils in boxes of p and q, then what is the highest number of pencils one cannot buy when <br><br>
2. p and q are relatively prime<br><br>
3. p and q are not... |
What is the greatest number of pencils that you cannot buy? |
The mate-in-two is
>! 1. Rb1+ Kxb1
>! 2. Qb2#
So the key is
>! ROOKBONEQUEENBTWO, which produces... no intelligible result when used.
>!
>! *However*, the board seems upside down -- white start on ranks 1-2 but the position makes a lot more sense if black pawns move up (although I think it's a legal posit... |
The infinite country of Saddlestania has some very interesting geography: its elevation from the mathematically flat sea level exactly follows the equation $$\mathbf{z=x^2-y^2}.$$
After traveling along the infinitely long, yet perfectly straight coastline, you arrive at Saddle Point, the only place in the country wh... |
The infinite country of Saddlestania has some very interesting geography: its elevation from the mathematically flat sea level exactly follows the equation $$\mathbf{z=x^2-y^2}.$$
After traveling along the infinitely long, yet perfectly straight coastline, you arrive at Saddle Point, the only place in the country wh... |
A shop sells pencils only in boxes of fixed size.
It cannot sell 100 pencils.
It can sell any larger amount of pencils.
It has one of each size box on display.
question 1: What is the minimum amount of boxes it may have on display?
question 2: What is the minimum amount of pencils it may have on disp... |
A shop sells pencils only in boxes of fixed size.
It cannot sell 100 pencils.
It can sell any larger amount of pencils.
It has one of each size box on display.
question 1: What is the minimum amount of boxes it may have on display?
question 2: What is the minimum amount of pencils it may have on disp... |
<sub>This is in the spirit of the [What is a Word/Phrase™][1] series started by [JLee][2] with a special brand of [Phrase™][3] and [Word™][4] puzzles.</sub>
-----------
If a word conforms to a special rule, I call it a Checkmate Word™.
Use the following examples below to find the rule.
| Checkmate Word™ ... |
Can this equation be solved with whole numbers? |
[This is from one of my friends, a year ago]
We have 6 weights: 2 red, 2 black, 2 blue. Of each color, there is one that's 100g and one that's 101g. How can you identify which ones are 101g, in two measurements, with a one-armed scale? |
Let's say we have a big box with inner edges with the lengths 2m, 1.5m, 1.4m.
Can we fill this with smaller boxes with the edge lengths of 3dm, 5dm and 1m, without any gaps? |
Alice and Bob live in London, UK. On a Friday, as per usual, Bob leaves for work before Alice. At lunchtime he receives a WhatsApp message from his friend Charles:
>*Sorry to cancel on you last week (hope you weren’t too BORED without us!). Rest assured, Denise and I are on for tonight, so we’ll be round at eight... |
The hints to what the list *actually* represents are:
>! the word "BORED" in all-caps, the four people getting together in the evening, and the formatting strangeness (the occasional lowercase letter in the list, plus the circled THX at the bottom).
These all give the secret real reason for the list:
>! this i... |
[![enter image description here][1]][1]
There are no horizontal word boundaries in the grid. Answers to "across" clues must be written on their correct row, in the order given, with no spaces.
Six "down" clues have had **one letter moved** from one word to another. This must be restored to its proper place before... |
You are going to a donut store, which donuts are more than 500 dollars. The most fancy one is the Donut Dedeluxe, which cost 5000 dollars.
Luckily, they have a 75% off which is now 1,250. But, you must hear the manager first.
They are gonna say a random sentence and you must answer a number. After you answer with... |
[![enter image description here][1]][1]
There are no horizontal word boundaries in the grid. Answers to "across" clues must be written on their correct row, in the order given, with no spaces.
Six "down" clues have had **one letter moved** from one word to another. This must be restored to its proper place before... |
[partial - missing one clue, and explanation for another]
The filled grid:
>! [![completed 15×15 grid][1]][1]
Clue explanations:
>! [![clue explanations and decompositions][2]][2]
The gimmicks:
>! The added letters spell **GEORGE** -- and indeed, he was a **BEATLE**, as spelled out by the moved letter... |
The first thing we need to do here is rearrange the 30 tiles in a meaningful way. We can do this by noticing:
>! That each run of letters is prefixed by one of 'F', 'S', 'T', 'FO' or 'FI', and suffixed by one of 'M', 'T', 'W', 'TH', 'F', 'S' or 'SU'. This is a combination of the first letters of an ordinal number (*... |
I decided to let my computer solve it, and it found the following solution:
>! 17, 18, 21, for a total of 56.
Assuming my program is correct, this is optimal. The second-best solution has box sizes that are coprime:
>! 13, 21, 23, for a total of 57.
Using 4 or 5 display boxes gives worse solutions:
>! 6,... |
<sup>*What follows here is a little Easter Egg hunt I've pulled together for you all this year. Ultimately, you need to discover **a single word of four letters in length** which will be revealed by the puzzle once all steps have been fully resolved.*</sup>
<sup>*Happy hunting, and Happy Easter!*</sup>
---
>... |
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