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.

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7
votes
2answers
321 views

How many squares can a limp queen move to?

Consider a large chessboard. A limp rook is a chess piece that moves one step orthogonally, but it turns $90$ degrees after every move. The limp rook makes some moves, not crossing over its own path, ...
2
votes
2answers
179 views

Quickest chess stalemate with Queens exchange

Continuing my previous puzzle. If both players cooperate, what is the quickest stalemate in chess that includes a Queens exchange, in a legal game?
6
votes
4answers
520 views

Generalization of the two-surgeons-two-patients-and-two-gloves puzzle

This is the original puzzle with $n=2$. I recommend solving it before this one to get acquainted with the mechanisms. There are $n$ patients in an hospital (let's call them $p_1 \dots p_n$), each of ...
3
votes
2answers
216 views

Quickest mate with Queens exchange

If both players cooperate, what is the quickest mate in chess that includes a Queens exchange, in a legal game?
-2
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0answers
142 views

9x9 grid containing the most words

Let's have a 9x9 grid. In the top row you can put any nine letter word. By permutating the letters of that word, fill the entire grid. The same letter should not appear more than once in any row or ...
5
votes
1answer
181 views

Insert Plus Signs and Add

If you take any integer (in base 10) and insert plus signs, "+", in between its digits (as few or as many as you like), and carry out the indicated sum, you will end up with a smaller number ...
-1
votes
1answer
122 views

A Complex Dash To Stalemate

For today's contribution to PSE, I present a sliding block puzzle! I have a series-helpstalemate in 26 for you all with a relevant question attached. The illegal position is intentional. Objective #1: ...
15
votes
2answers
1k views

An overcomplicated Boat Puzzle

Based on Xkcd's Boat Puzzle At the riverbank, a succession of people have given you a large lump of objects to transport across the river. These are: 101 cabbages 2 goats, one of which eats wolves 4 ...
6
votes
0answers
129 views

What's the best path through a garden that maximises the ground you can reach but minimises the steps taken?

I'm messing around with this toy problem I came up with. Say you have a yard that's 16 x 16 feet. Each square foot of the grid can either be a paving square for the path or a soil square for plants. A ...
4
votes
1answer
251 views

Choosing squares on a square board

I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
12
votes
2answers
1k 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. ...
12
votes
2answers
663 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, ...
0
votes
2answers
137 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 ...
6
votes
1answer
176 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
600 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
2answers
347 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 ...
14
votes
3answers
2k views

How many clues are required to ensure Einstein's Puzzle is solvable?

I used to play Einstein's puzzles a lot when I was younger, and very quickly learned to assess quite rapidly whether I thought a puzzle would be a quick solve or more time-consuming, but I never ...
2
votes
2answers
237 views

Grids with tiles of two colors and connectors

Make a square grid with an even side. Make a continuous trail which passes through all small squares; the trail ends where it started. Where there is an angle you can put a red or a blue tile. On ...
14
votes
2answers
478 views

Create a 1 meter measure

How many folding steps do you need to create a $1 \, \text{m}$ measure from an ideal DIN A0 sheet? This sounds easy, but consider that this paper has edge lengths of $\sqrt[4]{2} \, \text{m}$ and $\...
1
vote
2answers
107 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 ...
1
vote
2answers
328 views

Scheduling Meetings

I came across this problem in real life and thought it could be made into an interesting puzzle. I will enjoy seeing how my eventual solution could be improved! Here's the situation. There ...
0
votes
1answer
157 views

Mirror Mirror On The Board

Mirror mirror in the board Decipher the riddle of this horde How many moves to it, please? To put my brain at ease! Both sides help, follow their paths The solution you must craft Oh, and there is but ...
8
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
173 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 ...
18
votes
1answer
693 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.  ...
5
votes
1answer
198 views

Selfmate In How Few? #3-Unknown Limits

I dug up the below old position when going through a Google Docs document today. I know that it's supposed to be a somewhat winding, clearly dualed, selfmate. To be honest, I genuinely don't know the ...
6
votes
4answers
380 views

Crazy queen in checkers

Checkers Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
5
votes
2answers
533 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 ...
3
votes
1answer
186 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 ...
0
votes
4answers
708 views

Find the longest arithmetic expression with value equal to number of letters in its english representation [closed]

The expression "twenty minus five" has 15 letters (we ignore spaces) and also has the arithmetic value of 15. You can use standard math constants, operators and functions, represented by ...
13
votes
3answers
720 views

The Longest -1 Word

What is the longest -1 word (or the word worth most in Scrabble for words with the same amount of letters (which is just the addition of all the letter values of the original 'word', no constraints)), ...
0
votes
1answer
169 views

Selfmate In How Few? #2-Taking Flight

After my first one was solved so quickly, it's time for the next meal! It's another one that I created for the same mentioned site. Warning: this is a fairly long one, even with its simple strategy! ...
6
votes
4answers
269 views

Pawns and kings, what is the optimal play for white?

White to move. Source: wu riddles
3
votes
1answer
734 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 ...
7
votes
1answer
176 views

Rubik's Scramble Search

Find a scramble which will produce a Rubik's cube fulfilling the following criteria which uses as few turns of faces as possible (Half-Turn-Metric): Each of the six faces show exactly three colours ...
1
vote
1answer
3k views

How to swap adjacent corners?

I want to swap adjacent corners of U layer, the only thing I care is: position of other 6 corners. I don't care: orientation of all corners position of all edges orientation of all edges The goal ...
-4
votes
1answer
219 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. ...
14
votes
2answers
547 views

Minimum effort to detect a solved Rubik's Cube

When writing a program to permute a Rubik's Cube and then subsequently detect whether it is solved or not, what is the absolute minimum amount of programmatic effort required to determine if the cube ...
5
votes
1answer
166 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 $a_1$...
10
votes
4answers
888 views

Prime Circuit Optimisation

It's logic gates time! You are only allowed to use NOT, OR, AND, XOR gates, accepting 1,2,2,2 inputs respectively. PART ONE You must build a circuit with $n$ inputs, and 1 output. The output must be ...
7
votes
1answer
659 views

Lights in the Dungeon: Five by Five

This is the third in a series Lights in the Dungeon puzzles. previous (2nd) <-- | --> next (4th) You are practically skipping as you leave the four by four dungeon. This has been pretty easy so ...
22
votes
1answer
945 views

Peaceful Encampments

This math puzzle is due to Donald Knuth (as far as I know; maybe he got it from someone else) circa 2014. Consider a plain represented by the unit square. On this plain we want to “peacefully ...
7
votes
10answers
3k views

Word with the largest number of different phonetic vowel sounds

Which English word has the largest number of different unique phonetic vowel sounds in it? I will only count one vowel sound per syllable. To make it more like a competition, if two people get the ...
1
vote
1answer
86 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 ...
24
votes
0answers
2k views

Is there a move-efficient way to rotate the center pieces on the Octo-Star?

I'm looking for a more efficient algorithm to rotate the center column of the Octo-Star puzzle 45 degrees. The situation below occurs when four properly-oriented edges are next to each other, ...
4
votes
3answers
331 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 ...
9
votes
2answers
474 views

Third timer's a charm

Three motorized 24-hour light timers are arranged between a power outlet and a light bulb, with timer A parallel to a daisy chain of timers B and  C. For these timers, devise schedules that ...
1
vote
3answers
298 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
455 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
364 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 ...

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