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.
588
questions
12
votes
2answers
954 views
Laser and mirrors on a 4x4 grid
You are given an empty 4x4 grid. You can place some diagonal mirrors into the cells of the grid. You then fire a laser from some location outside of the grid. The laser travels in a straight line. ...
0
votes
2answers
131 views
How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day
My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team.
I have 150 open slots every day (5 days a week) for those 20 teams ...
11
votes
2answers
606 views
Introducing S-sequences: which is the shortest to contain all integers 1 to 20?
Consider a sequence (finite or infinite) of different positive integers, such as the following, in which the first term is 1, and thereafter the nth term is either the previous term plus n, minus n, ...
6
votes
1answer
162 views
42 lines on a chessboard with associated numbers
The 64 squares of a chessboard can be associated with 42 lines as follows:
the 8 rows
the 8 columns
13 diagonals from north-west to south-east
13 diagonals from north-east to south-west
Those ...
12
votes
1answer
591 views
All distances different on a chess board
Here is a simple formulation for, I believe, a quite difficult problem.
I have played with it, I don't have the answer yet.
The question: How many pawns can you put on a standard 8x8 chess board in ...
-2
votes
0answers
129 views
Trivial and non-trivial solutions on grids
Let's have a 10x10 square grid with 7 empty squares. This GRID is to be filled with skinny trominoes, with zero arrows pointing to the empty squares. The solution has to be non-trivial.
On the grids ...
2
votes
2answers
335 views
Minimum number of questions?
This is an interesting puzzle which I've been racking my brain to solve for some time. I've found different variations of this puzzle but it does not seem like this one has been asked before. Here it ...
1
vote
2answers
105 views
Alice and Bob play neighboring sums game version 2
Alice and Bob are playing the neighboring game
which is originally a single person game with the aim of getting the highest points at the end.
You start with an empty 4x4 grid. At each
turn, you can ...
7
votes
2answers
3k views
Social distancing in a 5x5 room [duplicate]
I have booked a square meeting room that is 5 by 5 meters. Our Covid-19 policy says that each person must be at least 1.5 meters away from any other person. What is the highest number of people that ...
3
votes
1answer
169 views
Some blissfully ignorant math?
I was playing around with the code for my game the other day in an effort to create some unique effects. One thing I created was what I called an "ignorant assignment" in which I applied ...
5
votes
2answers
527 views
A piece of paper repeatedly cut into 8 or 12 pieces
You are given a piece of paper. It will be cut into 8 or 12 pieces.
Each of those new pieces can be cut again into 8 or 12 pieces or left uncut. This process is (theoretically) repeated as often as ...
6
votes
4answers
256 views
-4
votes
1answer
213 views
The cow and the butcher
Let’s have 12 stalls spaced equidistantly, and a cow traveling between them. In the 12th stall a butcher is waiting with
a sharp knife. So the farthest stall a cow wants to reach is the 11th stall. ...
3
votes
1answer
726 views
Most efficient way for people along the edges of a grid to move to the center
I'm considering a $2k\times 2k$ square grid ($k\in\mathbb Z^+$) with $8k$ highly rational people standing along the vertices forming the perimeter. All of these people want to go to the centre of the ...
5
votes
1answer
163 views
Fold the plane four times to get the maximum number of cross points
You have a straight line $l$ in an infinite plane.
You can fold the plane along any straight line so the line $l$ becomes two rays with a common starting point. In the picture we fold along line $a_1$...
1
vote
1answer
85 views
How can I find the shortest path solution or even begin to finding the most optimal solution to a weld robot sequencing problem? [closed]
Not sure this belongs here, but I thought I'd ask: How should I come to an understanding of an optimal weld sequence for a weld robot that welds a physical item on a revolving carousel (the gray T ...
4
votes
3answers
329 views
Filling a grid with skinny trominoes which have arrows on their ends
Let's have a 10x10 square grid with 7 empty small squares. This grid is to be filled with skinny
trominoes which have arrows at their ends (see figure 1). What is the maximum number of arrows
which ...
18
votes
1answer
686 views
Spot that puzzle
This diagram solves an occasionally seen member
of a well-known family of optimization puzzles.
Spots ● generalize a component
that is represented variously in different statements of these puzzles.
...
1
vote
3answers
291 views
Egg drop problem for infinite floors [closed]
This is a modification of the infamous egg drop problem, which I have seen formulated as in the following manner:
Given $e$ eggs and a building of $f$ floors, how can we find the lowest floor at ...
10
votes
2answers
453 views
Clash of the Robinsons
"Ridiculous!" you think "What can be the odds? Either I'm hallucinating or the amateur writing this story plunged to new depths of incompetence." Both being equally likely you don'...
2
votes
1answer
360 views
A number like waldo?
What is the smallest whole number that when its individual digits are summed, produces a number 4 digits long? For example, the number $5357$ is no where close since $5 + 3 + 5 + 7 = 20$.
Note: I'm ...
3
votes
1answer
181 views
What is the most STAMINA-efficient strategy to escape the well?
You are roleplaying as an adventurer under the direction of a sadistic DM who has just thrown your character down a well.
In order to escape, you have unlimited chances at a STAMINA check, difficulty ...
3
votes
2answers
275 views
It's kind-of like Minesweeper
Have you ever played "Minesweeper" or "Lights Out!" and wondered what it would be like to reverse the process? Me too! Say hello to a 10 by 10 grid that I like to call "Number ...
2
votes
2answers
182 views
Powerful Octagon
Place different integers on the vertices of an octagon so that the sum of the integers in any two vertices joined by one of its edges is a power of 2. Do so in such a way that the largest integer used ...
4
votes
2answers
405 views
Longest chain of checks and captures
On a standard size chessboard, with white to move, make a configuration of chess pieces and moves, so that with every move by white the black king repeatedly becomes checked. With every move black ...
5
votes
5answers
499 views
Find the most unfortunate compact combination of coins to have in LOLandia
You live in LOLandia. Its currency is called 'lulz' and comes in the form of coins and paper banknotes. The smallest paper banknote has a nominal value of 500 lulz. There are six types of coins, each ...
11
votes
3answers
1k views
Attacking diagonal queens
What is the least number of queens you need to place on the main diagonal of a 8x8 chess board such that every square is under attack?
3
votes
2answers
276 views
Fix this puzzle, please!
My students claim that this disconnect four puzzle (fill the grid with crosses and zeros, such that no four equal symbols appear in a row. Rows can be horizontal, vertical, or diagonal) does not have ...
4
votes
1answer
214 views
My High School's Reunion
My high school is celebrating 30 years since graduating its first class and is planning to invite for lunch 20 alumni, 600 in all, from each of those classes.
Hosts are planning to sit everyone in ...
3
votes
0answers
100 views
Most leads in a "difficult" Sudoku
Since "difficult" is undefined, let me define it arbitrarily: A Sudoku is difficult if it can't be solved by only considering singles (naked or hidden), the most basic solving strategy.
How ...
0
votes
1answer
114 views
Does every validly posed Sudoku have at least one solution and if not what is the minimum number of givens for it to be unsolvable? [duplicate]
Does every validly posed Sudoku (doesn't break any Sudoku rules so only no duplicate 1 to 9 in rows, columns or square) have at least one solution, and if not, what is the minimum number of givens for ...
7
votes
0answers
204 views
Doubling the cube with rational Meccano strips
In three monographs published in 2006, 2008 and 2014 Gerard 't Hooft considered "Meccano mathematics": how to construct specified distances and regular polygons by a rigid system of ideal ...
9
votes
2answers
795 views
16 Step Switchover
The picture above shows two arrangements of four rectangular blocks, each labelled A to D. The arrangement on the left is the starting arrangement, the one on the right is the goal position. To solve ...
9
votes
1answer
330 views
Pythagorean triangle dissection
This is a variation of
Pythagorean quilts.
I will make it short, this time.
Pythagoras's theorem also works for triangles. This leads to the following variation:
Dissect the triangles of size 5 and ...
15
votes
3answers
954 views
A Perfect Diamond of Numbers
A diamond of numbers is an arrangement of circles in the shape of a trapezoid (see figure) in which the number in any circle above its central (longest) row is the sum of the two numbers in the ...
13
votes
7answers
2k views
Spiders on a cube
Two spiders are trying to catch an ant. All are constrained to move along the edges of a transparent cube. The speed of the ant is $1$. The speeds of the spiders are $v_1$ and $v_2$ respectively. What'...
3
votes
2answers
749 views
Most points on a circle
What is the most number of integer lattice points that lie on the circumference of a single circle whose radius is 80 or less? Please no computer computations.
5
votes
2answers
224 views
Most polyominoes on a Rubik's cube
What is the most number of distinct free polyominoes you can form on the faces of a standard 3x3x3 Rubik's cube? Here a polyomino is considered as a set of orthogonally-adjacent cells of the same ...
6
votes
1answer
808 views
Cutting off one's nose to spite one's eyes
Disclaimer: to keep graphic depiction of gratuitous violence to a minimum the face to be spited has been deliberately kept abstract.
You are required to further reduce any distress this puzzle may ...
3
votes
1answer
363 views
Using squares to prove e > 2.7
Edited to replace $\exp(-x)$ with $\exp(x)$. My apologies.
I loved this puzzle, so thought I'd submit a similar one:
The definite integral $\int_{−\infty}^{1} \exp(x)dx$ is equal to $e$ . Using ...
5
votes
2answers
258 views
Longest sequence of two-digit sum replacements
You are given a two-digit number. You can replace one of its digits with the sum of its digits modulo 10. For example, if the starting number is 58 then you can change it to 38 or 53. You can continue ...
104
votes
2answers
10k views
Prove that π > 3
It seems that once upon a time some politicians tried to pass a law fixing the value of π to be exactly 3. The idea being to "make math simpler so that our children can get better at math".
...
12
votes
2answers
429 views
Square Crayon Sticks
Ten sets of crayons forming all the digits from 0 to 9 can be moved, flipped, rotate and intersect without changing their digital forms. What is the maximum number of 1x1 stick squares that can be ...
2
votes
1answer
198 views
A solitaire Blokus problem on a rectangular board
Rules
As in Blokus, you have a total of 21 pieces (every piece from monomino to pentomino) in hand:
All of these polyominoes are free, this means that you can rotate or flip them as you wish before ...
5
votes
2answers
270 views
Five friends and two motorcyclists
Five friends Alice, Bob, Carole, Dylan and Emma are heading to a common destination 100 unit distance away. They start together. Grandma Alice walks at a speed of 1. Bob and Carole walk at speeds 4 ...
8
votes
2answers
289 views
What pieces does White need to beat Black's veto?
Consider the following chess variant: before each of White's moves, Black chooses one move which White is not allowed to make.
(The rules for which positions constitute checkmate are unchanged - Black ...
3
votes
1answer
126 views
Exchanging stones on a 8x8 board with sum of two adjacent numbers not being prime
You are given 64 stones labelled with number 1 to 64 each. All those stones are randomly placed on the squares of a 8x8 chess board such that each square is occupied with exactly one stone.
A move is ...
3
votes
1answer
255 views
Is there a minimum number of clues that every sudoku puzzle has?
I've seen that the fewest clues on a Sudoku board has been proven to be 17 but I'm wondering if it's possible for every board to have some combination of 17 clues or, if not, if there is a proven ...
3
votes
3answers
164 views
Rock climbing higher and faster
The Olympic rock climbing competition has 20 climbers. Each climber competes in 3 separate events, where they rank from 1st to 20th. The final score of a climber is the product of their rankings from ...
25
votes
3answers
4k views
Rock climbing at the Tokyo Olympics
The idea for this puzzle came from my friend Jan. The puzzle is based on real world events from the Tokyo Olympics.
The Olympic rock climbing preliminary round has 20 climbers. Each climber competes ...