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> There are $N$ chests with gold, silver and cooper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests and se... |
> There are $N$ chests with gold, silver and cooper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests and se... |
> There are $N$ chests with gold, silver and copper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
>
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests and... |
> There are $N$ chests with gold, silver and copper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
>
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests, th... |
> There are $N$ chests with gold, silver and copper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
>
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests, th... |
I'm amazed that, although well known, this problem hasn't been posted yet.
## Monty Hall ##
- You are on a game show.
- The host of the show shows you three doors.
- He tells you that behind one of them, is a new car, and behind the
other two is nothing (or in some versions of the story, a goat).
- He ... |
> There are $N$ chests with gold, silver and copper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
>
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests, th... |
> There are $N$ chests with gold, silver and copper coins in a dragon's cave. You see how many chests there are, but you have no idea how coins are distributed, and the clever dragon proposes you a hard game:
>
1. You must to chose and say a number (let's call it $M$).
2. Then you go and check out all chests, th... |
#Easily Divisible Treasure#
Lets assume that the treasure can be divided into any portions we want. This could be done with [coins of different values](http://puzzling.stackexchange.com/questions/186/whats-the-fewest-weights-you-need-to-balance-any-weight-from-1-to-40-pounds), or with a sufficient number of coins the... |
You meet a clever, and dark man. He wants to steal your mind and sell it to the dumbies (an imaginary species of shadows that have an IQ of less than -150)
He offers you to play a game, if you win, he'll give you +50 IQ, but if you lose, he gets 50 of your IQ. It's very tempting, so you listen to the rules and agree... |
The Impossible Test? |
Lets test the "If I were to ask you "is left is the correct path?" would you say "yok"?" question.
- Knave and yok=yes and left = correct
His answer is yok
- Knight and yok=yes and left = correct
His answer is yok
- Knave and yok=no and left = correct
His answer is yok
- Knight and yok=no and l... |
The Impossible Game? |
Imagine a 4x4 square with a picture you need to make with tiles in it, now imagine you can swap any 2 pieces next to eachother (horizontal, and vertical, not diagonal.) What's the maximum amount of moves needed for this type of game? What's the setup required for this game? Label it 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... |
What's the Maximum Moves Needed for this kind of Puzzle? |
Imagine a 4x4 square with a picture you need to make with tiles in it, now imagine you can swap any 2 pieces next to eachother (horizontal, and vertical, not diagonal.) What's the maximum amount of moves needed for this type of game? What's the setup required for this game? Label it 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... |
>Bob goes to a vending machine to buy a can of soda. He opens his wallet, and, to his surprise, has no dollar bills or any bills for that matter. The soda costs exactly $1 USD for that matter. Bob also has change in his wallet, but even still, he can't buy the soda. What is the maximum amount of change Bob can have wit... |
Here is a puzzle involving distrust and asymmetric knowledge. (It was inspired by, but not exactly following, the board game [The Resistance: Avalon][1].)
There are ten resistance fighters trying to overthrow the evil empire. Among them there is actually a secretive resistance leader, 5 loyal allies, 3 spies, and ... |
Here is a puzzle involving distrust and asymmetric knowledge. (It was inspired by, but not exactly following, the board game [The Resistance: Avalon][1].)
There are ten resistance fighters trying to overthrow the evil empire. Among them there is actually a secretive resistance leader, 5 loyal allies, 3 spies, and ... |
> There are $N$ chests with gold, silver and copper coins. You have to look inside the chests and select $M$ chests, that in total would have not less than 50% of all gold coins (that are in all $N$ chests) and not less less than 50% of all silver coins, and not less less than 50% of copper. What is the minimum $M$ to... |
> There are $N$ chests with gold, silver and copper coins. You have to look inside the chests and select $M$ chests, that in total would have not less than 50% of all gold coins (that are in all $N$ chests) and not less less than 50% of all silver coins, and not less less than 50% of copper. What is the minimum $M$ to... |
> There are $N$ chests with gold, silver and copper coins. You have to look inside the chests and select $M$ chests, that in total would have not less than 50% of all gold coins (that are in all $N$ chests) and not less than 50% of all silver coins, and not less than 50% of copper. What is the minimum $M$ to guaranty ... |
Abalone is a 2-player board game. Here's a brief explanation from [Wikipedia][1]:
The board consists of 61 circular spaces arranged in a hexagon, five on a side. Each player has 14 marbles that rest in the spaces and are initially arranged as shown below.
![][2]
For each move, a player moves a line of one, two... |
You cannot do it in any less than 30 moves.
If you were to move each marble individually, you'd need 88 moves to get them all to the other side.
* 4 moves each for moving the row of 3 marbles to the corresponding position on the other side
* 6 moves each for moving the row of 6 marbles to the corresponding posit... |
An attempt at the general problem: given a target value T and a number of denominations of coins x1, x2...xn (ordered from highest to lowest), find the maximum total of coins it's possible to have without being able to make exactly T.
If there is an xi which doesn't divide T exactly then you can have an unlimited numb... |
There's 16 buttons arranged in a 4 by 4 square. They are coloured either red, or green. They appear like this (red being 1, green being 0)
<1010
<0101
<1100
<0011
Each press will switch all the buttons diagonal of it, and the button on the exact opposite of it (for example the one exact opposite of the one in ... |
16 Buttons, Turn them all Red or Green? |
There's 16 buttons arranged in a 4 by 4 square. They are coloured either red, or green. They appear like this (red being 1, green being 0)
> 1010
> 0101
> 1100
> 0011
Each press will switch all the buttons diagonal of it, and the button on the exact opposite of it (for example the one exact opposite of t... |
Unfortunately for the knights, if N>3 there is no way for all of the knights to be next to all of their friends.
----------
Using oerkelens' logic, we can show that N=6 doesn't work:
. a . a . .
a . . b a b
. . A . . .
a . . . B .
. a b a . .
. . . b . b
Again, A has 8 friends a... |
There's a 4x4 square, where switches are either red or green. When you flip a switch, all the buttons on that row and column will alternate colours.
Are every starting position possible to complete? If not how many are there that are impossible?
**Note:** To complete all tiles must be green! |
Is it Always Possible? Colour Flipping |
There's a 4x4 square, where switches are either red or green. When you flip a switch, all the buttons on that row and column will alternate colours.
Are every starting position possible to complete? If not how many are there that are impossible?
**Note:** To complete all tiles must be green!
Letting 1s be red ... |
In [From knights to kings][1], we were asked
> On a NxN chess board $N^2$ knights are placed (one per cell). Each pair of knights, who control each other (i.e. one move away from each other) are friends.
One day all knights are promoted to kings. Is it possible to put them on the board (in different order) that all... |
You are on a quest to the find the lost kingdom of Acarien. On your way, you end up at a fork in the road. Both paths look exactly the same. At the junction sits a wise man. The wise man will only speak the words “*ça*” or “*ɠa*” meaning either *yes* or *no* (you don’t know which means which). The wise man will answer ... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
Unfortunately for the knights, if N>3 there is no way for all of the knights to be next to all of their friends.
----------
Taking oerkelens' logic just a bit farther, we can show that N=6 doesn't work:
. a . a . .
a . . b a b
. . A . . .
a . . . B .
. a b a . .
. . . b . b
Here... |
There's a 4x4 square, where switches are either red or green. When you flip a switch, all the buttons on that row and column will alternate colours.
Are every starting position possible to complete? If not how many are there that are impossible?
**Note:** To complete all tiles must be green!
Letting 1s be red ... |
There's a 4x4 square, where switches are either red or green. When you flip a switch, all the buttons on that row and column will alternate colours.
Are every starting position possible to complete? If not how many are there that are impossible?
**Note:** To complete all tiles must be green!
Letting 1s be red ... |
25 kids were in a class, they were all trading lunches.
* Each kid traded their lunch 5 times.
* At first 12 kids had bananas.
* At first 13 kids had oranges
* 16 kids like bananas
* 14 kids like oranges
* In the end 9 people threw out their lunch because they never liked it
So the question is, wha... |
Banana? Or Orange? |
A hunter wants to get on a bus, but belongings which have larger than 1 meter dimensions is not allowed.
So how will he be able to get his rifle (which is 1.5 meters) together with him without changing the shape of it ? |
Cut it in half? If you do it exact it will be the exact same shape but half as long, and therefore he will have two shapes that are 0.75m long (so no shape is breaking the 1.5 meter dimension rule), it might not be a clever read through the lines answer (the one you probably wanted) but with the way you have worded thi... |
You are stuck on an island and have been tasked by the natives with dividing a plate of chocolate into 4 equal pieces, one for each of the island's gods. Each god must have an equal share, or you go into the volcano.
The plate is a perfect square. The only tools you have are a short knife, a perfect circle with dia... |
OK, I did a computer search.
4x4 is too big for a brute-force search. Even for 3x4 I will need a night to complete.
But here are the maximum values for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 21
... |
OK, I did a computer search.
But 4x4 is too big for a brute-force search. Even for 3x4 I will need a night to complete.
But here are the maximum values for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 2... |
OK, I did a computer search.
But 4x4 is too big for a brute-force search. Even for 3x4 I will need a night to complete.
But here are the maximum values for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 2... |
What makes this a puzzle? The clock is broken!
The rules of this broken clock;
* Every second hour it is blank
* Every third hour the digits behind ':' are blank
* Every fifth hour the digits after the ':' are blank
* Every time the digits after ':' are a multiple if both 3 and 4 the digit after ':' is b... |
How Many Times will 1 Appear on the Clock? |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
OK, I did a computer search.
But 4x4 is too big for a brute-force search. The case 3x4 took a night to complete.
But here are the maximum values for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 21
... |
OK, I did a computer search.
But 4x4 is too big for a brute-force search. The case 3x4 took a night to complete.
But here are the maximum nb of moves for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 21 ... |
What makes this a puzzle? The clock is broken!
The rules of this broken clock;
* Every second hour it is blank
* Every third hour the digits behind ':' are blank
* Every fifth hour the digits after the ':' are blank
* Every time the digits after ':' are a multiple if both 3 and 4 the digit after ':' is b... |
You just got a new clock and it's broken. You're friend tells you he can fix it, but he needs a little bit of data from it. One thing he needs, his how many times 1 appears in the run of 2 days.
The rules of this broken clock;
* Every second hour it is blank
* Every third hour the digits behind ':' are blank
... |
How Many Times will 1 Appear on the Broken Clock? |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
##Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square i... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
You just got a new clock and it's broken. You're friend tells you he can fix it, but he needs a little bit of data from it. One thing he needs, his how many times 1 appears in the run of 2 days.
The rules of this broken clock;
* Every second hour it is blank
* Every third hour the digits behind ':' are blank
... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. His birth date fell on:
>! 1/9/39
His birthday ("magic day") was:
>! 1/9/78
Logic:
>! Obviously the... |
N is a number where every digit of N is divisible by it's place, for example:
> 1527
1 has to be divisible by 1, 5 divisible by 2, 2 divisible by 3, and 7 divisible by 4.
Additionally, N must be divisible by all of it's digits.
It has to be at least 5 digits long, and have at least 3 different digits.
Do... |
What is this Number? |
You are stuck on an island and have been tasked by the natives with dividing a plate of chocolate into 4 equal pieces, one for each of the island's gods. Each god must have an equal share, or you go into the volcano.
The plate is a perfect square. The only tools you have are a short knife, a perfect circle with dia... |
You are the praetor of _Tri_, a small triangular-shaped nation bordered on the northwest by the _Kingdom of Sauria_, on the northeast by the _Sultanate of Avia_, and on the south by the _Republic of Cryosta_, as shown below.
&n... |
I realize the 4x4 case has already been shown to not work, but let me try explaining it a bit differently -- a bit more "locally". Consider a large board, and we'll only look at the 4x4 corner of it.
In an actual 4x4 board, by symmetry there are only three kinds of pieces, a corner piece (like $A$), and edge piece ... |
I realize the 4x4 case has already been shown to not work, but let me try explaining it a bit differently -- a bit more "locally". Consider a large board, and we'll only look at the 4x4 corner of it.
In an actual 4x4 board, by symmetry there are only three kinds of pieces, a corner piece (like $A$), and edge piece ... |
I realize the 4x4 case has already been shown to not work, but let me try explaining it a bit differently -- a bit more "locally". Consider a large board, and we'll only look at the 4x4 corner of it.
In an actual 4x4 board, by symmetry there are only three kinds of pieces, a corner piece (like $A$), and edge piece ... |
I realize the 4x4 case has already been shown to not work, but let me try explaining it a bit differently -- a bit more "locally". Consider a large board, and we'll only look at the 4x4 corner of it.
In an actual 4x4 board, by symmetry there are only three kinds of pieces, a corner piece (like $A$), and edge piece ... |
I realize the 4x4 case has already been shown to not work, but let me try explaining it a bit differently -- a bit more "locally". Consider a large board, and we'll only look at the 4x4 corner of it.
In an actual 4x4 board, by symmetry there are only three kinds of pieces, a corner piece (like $A$), and edge piece ... |
N is a number where every digit of N is divisible by its place, for example:
> 1527
1 has to be divisible by 1, 5 divisible by 2, 2 divisible by 3, and 7 divisible by 4.
Additionally, N must be divisible by all of its digits.
It has to be at least 5 digits long, and have at least 3 different digits.
Does... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
His birthday ("magic day") was:
>! 1/9/78
Logic:
>! Obviously the... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
The birthday ("magic day") was:
>! 1/9/78
If the above is his DOB th... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
The birthday ("magic day") was:
>! 1/9/78
If the above is his DOB th... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
The birthday ("magic day") was:
>! 1/9/78
If the above is his DOB th... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
The birthday ("magic day") was:
>! 1/9/78
If the above is his DOB th... |
If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?
Well, here's one possible solution. The birth date fell on:
>! 1/9/39
The birthday ("magic day") was:
>! 1/9/78
If the above is his DOB th... |
OK, I did a computer search.
But 4x4 is too big for a brute-force search. The case 3x4 took a night to complete.
But here are the maximum nb of moves for smaller sizes:
1 2 3 4 5 6 7 8 9 10
+-------------------------------
1 | 0 1 3 6 10 15 21 28 36 45
2 | 1 4 9 14 21 ... |
#Reiterate problem
Bunny: a chess piece which moves like a bishop but only one square from its current position. It may also hop over another piece.
Hop: a bunny hops when another piece is in a square touching the current square (no diagonals). In its turn it occupies the square 3 squares from its current square in... |
This is where yesterday follows tomorrow, departure follows arrival, front follows back, start follows end, past follows future and even life follows death.
What is it? |
Sorry for not solving it completely, but I think it helps. There can be no certainty, rather a probability of the good guys winning. Obviously there's an upper bound of 5/6, since whatever happens, they can kill a random good guy in case he's the leader.
But other than that, any decision is tricky, since there's an... |
in December 1496, after a rainy day, an inn somewhere in the Black Forest, on one of the major north-south roads, was visited by a group of highwaymen in the middle of a freezing cold night. Fortunately, a band of adventurers present at the inn managed to fend them off. Because of the bounty on the highwaymen, they wan... |
Can you arrange 7 trees so that there are 6 rows of 3 trees? It is entirely possible.
**Note: A tree can be part of more then one row, for example a if you arranged a 3x3 square (9 trees) the tree in the center is part of 4 rows.**
Rows are usually horizontal but in this case they can be horizontal, vertical, or ... |
You roll 5 dice and I'll always be able to give a number uniquely-defined by your 5 rolls. You have to figure out how it works ~ without looking it up. Here's a couple example rolls:
1,2,3,4,5 = 6
3,6,2,3,1 = 4
If you need any more rolls to determine the answer, comment them.
Please try not to look it up, a... |
You roll 5 dice and I'll always be able to give a number uniquely-defined by your dice. You have to figure out how it works ~ without looking it up. Here's a couple example rolls:
1,2,3,4,5 = 6
3,6,2,3,1 = 4
If you need any more rolls to determine the answer, comment them.
Please try not to look it up, and ... |
You roll 5 dice and I'll always be able to give a number uniquely-defined by the numbers on the dice. You have to figure out how it works ~ without looking it up. Here's a couple example rolls:
1,2,3,4,5 = 6
3,6,2,3,1 = 4
If you need any more rolls to determine the answer, comment them.
Please try not to lo... |
Consider the following building floor plan, with a set of rooms labeled **A**-**G** and an **Outside**:
&nb... |
Find the shortest chess game with 18 queens? |
in December 1496, after a rainy day, an inn somewhere in the Black Forest, on one of the major north-south roads, was visited by a group of highwaymen in the middle of a freezing cold night. Fortunately, a band of adventurers present at the inn managed to fend them off. Because of the bounty on the highwaymen, they wan... |
#96 Half-moves:#
1.e4 f5 2.e5 Nf6 3.exf6 e5 4.g4 e4 5.Ne2 e3 6.Ng3 e2 7.h4 f4 8.h5 fxg3
9.h6 g5 10.Rh4 gxh4 11.g5 g2 12.g6 Bg7 13.hxg7 g1=Q 14.f4 h3 15.f5 h2
16.b4 a5 17.b5 a4 18.b6 a3 19.Bb2 Ra7 20.bxa7 axb2 21.a4 b5 22.a5 b4
23.a6 b3 24.c4 h1=Q 25.c5 h5 26.c6 Bb7 27.cxb7 c5 28.d4 c4 29.d5 Nc6
... |
#96 Half-moves:#
1.e4 f5 2.e5 Nf6 3.exf6 e5 4.g4 e4 5.Ne2 e3 6.Ng3 e2 7.h4 f4 8.h5 fxg3
9.h6 g5 10.Rh4 gxh4 11.g5 g2 12.g6 Bg7 13.hxg7 g1=Q 14.f4 h3 15.f5 h2
16.b4 a5 17.b5 a4 18.b6 a3 19.Bb2 Ra7 20.bxa7 axb2 21.a4 b5 22.a5 b4
23.a6 b3 24.c4 h1=Q 25.c5 h5 26.c6 Bb7 27.cxb7 c5 28.d4 c4 29.d5 Nc6
... |
#96 Half-moves:#
1.e4 f5 2.e5 Nf6 3.exf6 e5 4.g4 e4 5.Ne2 e3 6.Ng3 e2 7.h4 f4 8.h5 fxg3
9.h6 g5 10.Rh4 gxh4 11.g5 g2 12.g6 Bg7 13.hxg7 g1=Q 14.f4 h3 15.f5 h2
16.b4 a5 17.b5 a4 18.b6 a3 19.Bb2 Ra7 20.bxa7 axb2 21.a4 b5 22.a5 b4
23.a6 b3 24.c4 h1=Q 25.c5 h5 26.c6 Bb7 27.cxb7 c5 28.d4 c4 29.d5 Nc6
... |
in December 1496, after a rainy day, an inn somewhere in the Black Forest, on one of the major north-south roads, was visited by a group of highwaymen in the middle of a freezing cold night. Fortunately, a band of adventurers present at the inn managed to fend them off. Because of the bounty on the highwaymen, they wan... |
This is known as the "18-Queens Problem".
I found this well-known solution by Friedrich Burchard & Friedrich Hariuc (1976) in ***96 Half-moves***.
I can't make a claim to its optimality, but by looking at it and seeing that no better can be found, I'd say it may well be optimal.
1.e4 f5 2.e5 Nf6 3.exf6 e5 4.... |
> Some number of gold, silver, and copper coins are scattered in $N$ chests. You can look inside each chest and count each type of coin and then select $M$ chests. Your goal is to have at least 50% of all gold coins, at least 50% of all silver coins, and at least 50% of all copper coins. What is the minimum $M$ that wi... |
> Some number of gold, silver, and copper coins are scattered in $N$ chests. You can look inside each chest and count each type of coin and then select $M$ chests. Your goal is to have at least 50% of all gold coins, at least 50% of all silver coins, and at least 50% of all copper coins. What is the minimum $M$ that wi... |
A king sent 10 of his servants to buy him each 10 gold rings (100 gold rings in total). Each ring should weigh 10 gram.
One of his spies told him that one servant cheated and brought 10 rings each of 9 grams. Unfortunately, he couldn't recognize the face of the servant and that left the king wondering who is the the... |
So I have a question for you all, it's probably not too hard for you but it's relatively simple:
**How many times does *variable* appear?**
The hint for the variable is pretty short too:
*I am very small, you think of me little, you can find me in many places, even though I'm tiny. I am even in here.*
I'll ... |
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