Questions tagged [optimization]
A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.
657
questions
4
votes
1
answer
107
views
A robot that doesn't repeat move triplets
A robot is placed on an empty infinite grid. Each turn it can move in one of four directions: left (L), up (U), right (R) or down (D). It cannot move to a cell that it already visited. Also it cannot ...
- 26.8k
8
votes
0
answers
104
views
What is the shortest chess game with 30 distinct captures (PxP, PxN, PxR, etc...)?
In chess, there are 6 types of pieces that can capture other pieces, and there are 5 types of pieces that can be captured. Ignoring piece color, this means that there are thirty distinct possible ...
- 81
5
votes
0
answers
85
views
Diagonal pattern for 4x4x4 Rubik Cube with all colors on each side?
I love creating patterns on my 4x4x4 cube, so I came up with the idea to create the following pattern:
all sides have a diagonal pattern, meaning something like
...
- 151
5
votes
1
answer
194
views
Near Magic Squares with the First 25 Primes
There are 25 primes smaller than 100. What is the closest to a 5 x 5 magic square I can construct with them? By "closest" I mean the one with the most columns, rows, and diagonals (12 in all)...
- 14.9k
33
votes
6
answers
2k
views
Packing pentominoes in a circle
You want to prepare a pizza of 12 flavors. You have 12 oddly-shaped pieces of cheese that you decide to use for the pizza. The shapes happen to be ...
Oh, well, forget it! This isn't going to be ...
- 22.5k
17
votes
2
answers
915
views
He Hauls Hydra Heads across Hilbert's Hexagonal Hotel
(Special thanks to greenturtle3141 for providing an intriguing narrative backstory to my puzzle.)
To aesthetically appeal to his customers, Hilbert has recently redesigned his hotel. You see, all ...
- 313
1
vote
1
answer
168
views
Shortest algorithm to rotate 2 corners on a Rubik's Cube
I'm looking for the shortest algorithm to rotate 2 corners without rearranging any other pieces location or orientation. For example, turning the Top-Front-Right corner clockwise and the Top-Front-...
- 49
2
votes
0
answers
134
views
Shortest Algorithm to flip 2 edges on a Rubik's cube
I'm looking for the shortest algorithm to flip 2 edges without rearranging any other pieces location or orientation. For example, flipping the Top-Front edge and the Top-Right edge. My current best is ...
- 49
3
votes
2
answers
371
views
What's the minimum number of airplanes needed for one to make a round-the-world trip?
Inspired by this puzzle.
You have many airplanes starting at the same airport. Each plane has a fuel tank that holds just enough fuel to allow the plane to travel $\frac{1}{10}$ the distance around ...
- 5,187
11
votes
2
answers
3k
views
Sharing 41 sticks among 42 people
Question: Ali-Baba is a prisoner of the $42$ thieves who have just stolen $41$ identical magic incense sticks. The thieves want share this loot in such a way that everyone has exactly the same pieces ...
- 113
11
votes
4
answers
1k
views
Prime lights out
You start with a 4x4 grid filled with zeroes. If you press a cell then the cell and all its neighboring (horizontally and vertically) cells will have their numbers increased by 1. What is the most ...
- 26.8k
1
vote
1
answer
118
views
Diversified Rubik's Cube [duplicate]
I have, cleverly I hope, shuffled my Rubik's Cube for a while. I could not find a position where, for each faces, all colors appear 3 times or less. I always had a or several faces with at least 4 of ...
- 5,797
0
votes
1
answer
153
views
Puzzle regarding 100 random objects of different sizes, and choosing one at random one at a time to get largest
Basically, the riddle at hand was used to demonstrate a principle (of which I forgot), and it was asked thusly; I know there are other forms of it, but here goes:
You are fishing in a pond of 100 fish ...
- 3
2
votes
1
answer
349
views
Largest word tree
I was inspired by this awesome puzzle. Here is an image of a word tree borrowed from there:
In a word tree every path from the root to the leaves must form a distinct word. The size of the tree is ...
- 26.8k
0
votes
1
answer
152
views
Number of 6-person events so all groups of 3/10 people have dined together [closed]
Assume 10 people numbered 1-10 have to be invited for dinner events. However, the hotel can accommodate only 6 at a time. Therefore, they will be invited in batches until all groups of 3 people have ...
- 103
9
votes
11
answers
1k
views
Ten Pills in Ten Countries [closed]
You're about to leave for an international vacation where you'll be visiting ten different foreign countries. To make sure you don't catch any local diseases, your doctor has given you ten pills and ...
- 686
8
votes
3
answers
938
views
Chess lead change
Given the following Chess piece relative values and such that both players cooperate, what is the fastest way such that White first has an advantage of at least +10 piece value then secondly, Blacks ...
- 5,797
2
votes
1
answer
106
views
What is the name of this problem about maximizing the accepted offer from consecutive offers?
There was a problem I have read more than 15 years ago. I just remember the problem and the rough outline of the solution, and I would like to know if it has a canonical name to look up the ...
17
votes
7
answers
1k
views
Efficient Mowing at PSE
Your task:
Find the most efficient mowing path around the dark green bushes that mows (passes over) all of the grass (light green).
For those who cannot view the image above, there are 9 rows of 16, ...
- 17.5k
5
votes
2
answers
214
views
Robot painting a $K_5$
A robot starts at a node of a fully connected graph of 5 nodes (shown below). Each turn the robot can move across an edge and paint it in one of two colours - blue for odd turns and red for even turns....
- 26.8k
8
votes
4
answers
953
views
Yet Another Card Payoff Game
From A Practical Guide to Quant Interviews:
A casino offers yet another card game with the standard 52 cards (26 red, 26 black). The cards are thoroughly shuffled and the dealer draws cards one by ...
- 603
7
votes
1
answer
194
views
13 scales and a ... fake scale
You are given 14(*) scales that look and feel identical.
The scales are 2-pan scales. When you put stuff on each pan, the scale indicates whether both sides balance, and if not, which side is ...
- 22.5k
4
votes
0
answers
176
views
Mr. Bean's Ridiculous Way to Work
If you saw Mr. Bean as a kid, or ever, you know how crazy and unbelievable he is. In this scenario, Mr. Bean lives in the bottom left house and works for the school at the left, but he always takes ...
- 1,133
9
votes
2
answers
280
views
Largest set of factorials whose product is a perfect cube
Just one number must be removed from the set of integers between 1 and 100 (inclusive) so that the product of the factorials of the remaining numbers is a perfect square.
What is the least number of ...
- 14.9k
3
votes
3
answers
304
views
Checkmate N Kings with M Knights Perfectly
We have this Existing Puzzle which has got the valid and invalid cases listed ; the Accepted Answer is along the lines of what is invalid and what is valid.
But there was a flaw or fault in the Puzzle ...
- 4,808
9
votes
2
answers
991
views
Factorials whose product is a perfect cube
Find two or more different positive integers the product of whose factorials is a perfect cube.
How small can the largest of these be?
How few can they be?
- 14.9k
14
votes
3
answers
2k
views
Checkmate N Kings with M Knights
There are N White Kings on the Chess Board.
There are M Black Knights.
There is no Black King and no other Piece. Only M+N Squares are occupied.
Each White King is attacked by atleast 1 Black Knight, ...
- 4,808
19
votes
3
answers
1k
views
The universal ticket
I am submitting a very interesting problem from a French mathematical recreation site:
http://www.diophante.fr/problemes-par-themes/g-probabilites/g2-combinatoire-denombrements/1434-g248-le-billet-...
- 702
3
votes
2
answers
455
views
The longest path of edges on a 3x3 grid
A robot is placed on some vertex of a 3x3 grid. At each move the robot can take one step (up, down, left or right) along the edge of the grid to the adjacent vertex, but it cannot go outside the grid. ...
- 26.8k
26
votes
6
answers
5k
views
Checkmate 30 kings with rooks
Using only kings, and as few rooks as possible, set up a position where 30 of black's kings are checkmated.
Checkmate:
The king is in check
The king has no moves out of check
Black only has kings, ...
3
votes
3
answers
494
views
Multi-colored polyominoes inside a 7x7 grid
Can you place four red trominoes, four green tetrominoes and four blue pentominoes inside an 7x7 grid, such that:
No two polyominoes overlap
No two polyominoes of the same color touch each other ...
- 26.8k
8
votes
1
answer
193
views
Tetromino in a Pentomino Lair
Inspired by this question:
Can you fit twelve pentominoes (not necessarily distinct) and one tetromino inside a 10 x 10 grid such that they do not overlap or touch each other orthogonally (...
- 125k
10
votes
3
answers
1k
views
Fitting pentominoes inside a 10x10 grid
What is the most number of pentominoes that you can fit inside a 10x10 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically)?
Bonus: what is the most number ...
- 26.8k
4
votes
2
answers
323
views
Four pipes on a 8x8 grid
You are managing the construction of 4 water pipes on a 8x8 grid. The rules are the following:
Each section of a pipe uses a whole grid cell. Pipes are composed of multiple sections connected ...
- 26.8k
13
votes
4
answers
1k
views
The Game of Golden Squares
On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
- 5,187
9
votes
3
answers
544
views
Coloring the squares
You can choose from 4 colors to color every square of the following $10\times 10$ grid.
After you finish, I'm going to take a connected block with at most three colors away. Your goal is to minimize ...
- 5,187
4
votes
2
answers
262
views
Helpmate part 2
This is the second part of Fastest way to helpmate
You have been given the task to checkmate/helpmate black in fastest possible way in following ways:
Pawn promoting to only queen
Pawn promoting to ...
- 1,095
0
votes
0
answers
74
views
Disguising a Rubik's Cube rotation
I'm wondering if there's a way to disguise the total rotation of a Rubik's Cube? For example, if I wanted to rotate the (solved) cube I could obviously just apply a 90 degree yaw rotation. However, I ...
4
votes
3
answers
286
views
8x8 Grid with no parallels
In the 8x8 grid graph shown below;
you can put points to the edge of grid as shown below (blue dots).
The example above has 4 points and you construct a line between two points as shown below;
so ...
- 28.9k
0
votes
2
answers
155
views
Two triangles in a circle
This puzzle is inspired by this great puzzle.
You are given a circle. You can draw two non-overlapping triangles of any size and shape inside that circle. What is the highest percentage of the circle ...
- 26.8k
20
votes
4
answers
2k
views
Moving around a plane
A small plane went through some heavy turbulence and all its passengers ended up in the wrong seat. Now they need to get back to their assigned seats. The image below shows the map of the plane. The ...
- 26.8k
6
votes
2
answers
206
views
Splitting the integers 1 to 36
Split the integers 1 to 36 into two sets, A and B, such that any number in set A has a common divisor greater than 1 with no more than two other numbers in A, but for every number in B there are at ...
- 14.9k
14
votes
4
answers
1k
views
The mower's challenge
Weeds have taken over the roads. If mowed, they don't grow back, but unmowed weeds spread at speed 1 along the road. What's the minimum speed of the mower to get rid of all weeds? Roads are connected ...
- 5,187
3
votes
1
answer
317
views
How many distinct pentominos can be placed on a 8×9 board?
Upon proving optimality of an 8-pentomino solution for an 8×8 board, I was curious to see whether there is a 9-pentomino solution for an 8×9 board, namely a way to arrange 9 distinct pentominos within ...
- 1,085
14
votes
3
answers
2k
views
How many distinct pentominoes are possible to place on an 8 x 8 board?
Rules
Place some pentominoes into an 8 x 8 grid. They do not touch each other. They can touch only diagonally (with corner).
Pentominoes cannot repeat in the grid. Rotations and reflections of a ...
- 141
13
votes
2
answers
467
views
Put three pieces of cake into a round box
You're about to cut three pieces from a large cake to put in a round box of radius 1. If the pieces must be congruent triangles, and cannot overlap, what shape gives you the maximum amount of cake?
- 5,187
5
votes
4
answers
1k
views
Six positive integers
Find six different numbers (positive integers) such that each of them has a common divisor with precisely three of the other numbers. How small can the largest of the six numbers be?
What if $2n$, $n&...
- 14.9k
8
votes
0
answers
525
views
What is the longest Wordle game?
If you play Wordle in hard mode, with unlimited guesses, then you must solve any puzzle eventually. This is true because there are only a finite number of valid five-letter words, and it is not ...
- 181
2
votes
2
answers
366
views
Choose the wine
I based this on a problem from a mathematics presentation, adding a small twist. I did not readily find it here.
Your friend comes to dinner and you know he loves to drink Beaujolais. You have 'Cote ...
2
votes
1
answer
154
views
Hitting twice with different choices
This game of two players has public parameters an integer $n\ge2$, and a probability $p$ with $1/n<p\le1$. E.g. $n=4$, $p=1/3$.
In the first phase of a game, a player secretly decides $n$ ...
- 383