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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Shortest time to cook burgers

Attribution: I remember seeing this type of question some time ago but don't remember from where. So I have redesigned the question. Hope that is OK. You have 5 burger patties to grill. Each side ...
RogerA's user avatar
  • 6,049
1 vote
0 answers
172 views

Ma Drasi and her kitchen in need of paralyzation

I visited Ma Drasi's kitchen today, and it was a hot mess, both temperamental and situation-wise. The rooks were rattling, cooks were crying, snooks were shattering, and crooks were flying and defying!...
Rewan Demontay's user avatar
10 votes
4 answers
1k views

Painting a Checkerboard

I love checkers - but I've played it so much that the color of my board is faded and dull. Today, I resolved to paint it. Unfortunately, I slipped and fell :( Now there's paint all over my ...
BaileyA's user avatar
  • 681
11 votes
2 answers
523 views

A balanced banquet

As your king's fitness adviser you have been tasked with optimising His Majesty's diet. This entails making sure that the king eats equal amounts of carbs (rooks), fat (bishops) and protein (knights). ...
loopy walt's user avatar
  • 21.2k
6 votes
4 answers
753 views

How to Divide 1,987 Gold Coins Among 40 Pirates?

There are 40 pirates, designated as P1, P2, ...... P40, respectively. They aim to divide 1,987 gold coins using a two-stage division scheme: In the first stage, P1 initially splits all the coins into ...
Pumbaa's user avatar
  • 938
8 votes
4 answers
888 views

Smallest rectangle to put the 24 ABCD words combination

Put in the smallest possible size board all combination of 4 quantity of letters. Crossword must be connected. And can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters Example for:...
Rodolfo Kurchan's user avatar
14 votes
2 answers
1k views

Drowning Squirrel

On a super foggy day, a squirrel falls from a tree into a swimming pool. Due to fog, it cannot see any bank of the pool, unless it touches the bank. It is aware that the swimming pool is in the shape ...
thisIs4d's user avatar
  • 1,083
6 votes
3 answers
2k views

The Biggest Chess Blunder

Everyone knows that sinking feeling when you blunder your queen in one move, but it could be worse. In the position above, Black plays Nf7. This blunders a knight in one move, as well as a bishop-...
ApexPolenta's user avatar
  • 2,690
5 votes
2 answers
1k views

The best scoring REVOLVER

The initial setup a chess game creates this layout: P P P P P P P P R N B Q K B N R If we change the symbol each piece is represented by, something interesting ...
Rewan Demontay's user avatar
4 votes
2 answers
339 views

A safe with 4 locks

You are trying to open a safe. There are 4 locks and 4 keys (red, green, blue and yellow). When you insert the keys into the locks, the safe will make k beeps, where k is the number of keys that are ...
Dmitry Kamenetsky's user avatar
6 votes
2 answers
710 views

Attacking Hyenas

$N$ Hyenas are standing on a plane region in a forest. At $t=-1$, they see dead meat nearby. Being selfish, at $t=0$, each Hyena attacks the Hyena which is closest to it. All pairwise distances ...
thisIs4d's user avatar
  • 1,083
14 votes
3 answers
2k views

Wizard of subsets

Can you change this into this in three moves? You are the wizard of subsets. With only your mind, you can grab any subset of the 16 stone blocks and move them one unit in any direction (north, ...
SlowMagic's user avatar
  • 13.8k
13 votes
2 answers
3k views

What's the most distant chess position?

It's well known that the combinatorial explosion means that there are many, many, possible chess games. And yet most games are decided within 100 moves, and Wikipedia says that the longest tournament ...
Spitemaster's user avatar
  • 1,273
7 votes
4 answers
2k views

Fair d5 with as few faces as possible

Challenge: design a polyhedral die that will always give one of five outcomes, each with equal probability. While achieving that, minimize the total number of faces of the die. Think of the die as ...
isaacg's user avatar
  • 6,944
12 votes
3 answers
1k views

Mixing liquids in bottles

You have 3 identical bottles with a capacity of 4 litres: The first bottle contains 2 litres of liquid A The second bottle contains 3 litres of liquid B The third bottle contains 4 litres of liquid C ...
Dmitry Kamenetsky's user avatar
17 votes
3 answers
2k views

Most polyominoes in an 8x8 grid

What is the most number of distinct free polyominoes you can form by painting an 8x8 grid in two colours? Here a polyomino is a set of orthogonally adjacent cells of the same colour, so polyominoes of ...
Dmitry Kamenetsky's user avatar
6 votes
2 answers
352 views

Boxeslayers to the rescue

This is about layering boxes, not about slaying them. We have 1,830 2×5 boxes to stack safely as 10 alternating contiguous layer patterns of 183 boxes each. Layers have identical silhouettes that fit ...
humn's user avatar
  • 21.9k
35 votes
5 answers
3k views

A Queen and her Pawns

Place a queen and as many pawns as possible on a chessboard so that the queen has just one way of capturing all the pawns in precisely as many moves as there are pawns. Pawns do not move and do not ...
Bernardo Recamán Santos's user avatar
3 votes
1 answer
296 views

Smallest 3x3 Magic Square of different square sums

Consider the follow magic square highlighted in yellow. The sum of its rows and columns are in green and the sum of the diagonals in red. All of its sums are a square number with the sum of the whole ...
Maff's user avatar
  • 621
4 votes
1 answer
255 views

Farthest From Backgammon

This puzzle is part of the Monthly Topic Challenge #7: Board games. The famous Backgammon game can be seen as being played on a number axis with one player on the non-negative side (from 0 to 25) and ...
Scratch---Cat's user avatar
7 votes
2 answers
402 views

Smallest square that can pack thin digits

If we draw the digits 0 to 9, segmented into squares, across a rectangle of 2x5 (except the 1) they use up 81 total squares. Is it possible to pack them all into a 9x9 grid. What is the smallest n by ...
Maff's user avatar
  • 621
3 votes
2 answers
226 views

From white to black

This puzzle is part of the Monthly Topic Challenge #7: Board games. Place a knight on each of the white squares on the 8x8 chessboard. That would make a total of 32 knights. Is it possible to use a ...
Scratch---Cat's user avatar
2 votes
2 answers
422 views

A bit complicated 20 card games v2

this is follow up question of A bit complicated 20 card games. As the person who determines the order of the cards without changing the numbers on them, you want to make it more difficult for the ...
Oray's user avatar
  • 30.3k
3 votes
1 answer
347 views

A bit complicated 20 card games

In the game of 20-card games, the objective is to select a card or pass on it at every turn, with the goal of maximizing the sum of the numbers on the chosen cards. You have knowledge of the numbers ...
Oray's user avatar
  • 30.3k
-4 votes
2 answers
141 views

Smallest rectangle that fits the first 10 rectangles [closed]

What is the area of the smallest rectangle that can fit 10 rectangles with areas 1 to 10, inclusive? Rectangles must have integer sides and cannot overlap.
Dmitry Kamenetsky's user avatar
12 votes
4 answers
3k views

11 cyclists in a race

A team of $11$ cyclists begin a race. If each cyclist rides individually then their respective race times will be $10, 11, \ldots, 20$ minutes. However, if three cyclists with individual times $(a, b, ...
Dmitry Kamenetsky's user avatar
5 votes
1 answer
563 views

Sorting five plates

You have a stack of 5 plates of different sizes as shown in the left figure below. In each move you can pick up the top k plates (k is from 1 to 5) and flip them over. For example, if you do this with ...
Dmitry Kamenetsky's user avatar
4 votes
5 answers
592 views

How much can rounding up help you?

I go to a very fair university that likes to make sure that every student gets their best shot. One way they ensure this is by their rounding system. The rules are as follows: All marks for all ...
Simd's user avatar
  • 7,845
1 vote
1 answer
134 views

Maximum and minimum numbers of combinations in a double Latin Square

Let's have a double 6x6 Latin Square (see Figure 1). You can see that this Latin Square has thirteen combinations (see Figure 2). Can you make a double Latin Square that contains the maximum number of ...
Vassilis Parassidis's user avatar
4 votes
2 answers
247 views

5-digit numbers with at most one digit in common

5-digit numbers are created using the digits 1, 2, 3, 4, and 5. Any two numbers can have at most one corresponding digit equal to each other. How many different 5-digit numbers can you get in total ...
Oray's user avatar
  • 30.3k
9 votes
3 answers
452 views

PSE Advent Calendar 2022 (Day 17) Priority polar problem

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > Dear ...
Retudin's user avatar
  • 8,601
14 votes
5 answers
3k views

Dividing a square field into 5 equal regions

A farmer has a 10m x 10m field that has fences around the perimeter. What is the least number of 1m fences he needs to add to divide the field into 5 regions of equal area?
Dmitry Kamenetsky's user avatar
5 votes
2 answers
700 views

Bow or lazy checkmate?

Suppose that both players cooperate, find the shortest, in terms of number of moves, black checkmate such that the game is valid and white pieces never go on rows 4 to 8. e.g. ...
JKHA's user avatar
  • 6,033
5 votes
1 answer
600 views

Is "Connect 4 is Excellent, Connect 3 is Great" a solved game?

Connect 4 is known to be a solved game. I am introducing the Connect 4 is Excellent, Connect 3 is Great, variant of Connect 4. Both players play like connect 4 and fill the grid i.e. they don't stop ...
JKHA's user avatar
  • 6,033
5 votes
3 answers
428 views

Laziest Checkmate

Consider a game of chess where White delivers checkmate in their $X^{th}$ move. For all the pieces that remain on the board at the end of the game, consider their Manhattan Distances from their ...
Manish Kundu's user avatar
  • 2,704
4 votes
1 answer
182 views

Packing the Primes

Here is a 5x4 rectangular wordsearch (area 20) containing the primes between 1 and 100, {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} (numbers in any ...
Amoz's user avatar
  • 26.9k
38 votes
8 answers
4k views

The Bee Lover's Hotel

Dr Bees likes bees. Dr Bees is not his real name, but that is what everybody calls him. I should actually say that he is obsessed with bees. Bees are his whole life. He knows everything about them. ...
Florian F's user avatar
  • 29.8k
12 votes
1 answer
381 views

25 distinct numbers in a 6x10 Minesweeper grid

You are making a new Minesweeper game. You can place 1, 2 or 3 mines in a cell. As usual the number in an empty cell is the number of mines surrounding it (in 8 directions). Can you place mines into a ...
Dmitry Kamenetsky's user avatar
3 votes
1 answer
172 views

The longest shortest sequence of series moves

Being inspired, I concoct a question. It starts from a set chess board with only the White pieces. Chess problems in which only one side moves are called seriesmovers. What is the longest shortest ...
Rewan Demontay's user avatar
2 votes
1 answer
260 views

Cow Training Farm

Other than ordinary farms like Animal Farm, there is a farm called 'Cows Training Farm', which is a farm that trains $15$ very orz cows. Each year, six cows are chosen to join a competition. Mason is ...
Culver Kwan's user avatar
  • 5,600
13 votes
1 answer
1k 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 ...
Dmitry Kamenetsky's user avatar
14 votes
1 answer
399 views

What is the shortest chess game with 30 distinct captures (PxP, PxN, PxR, etc...)?

Progress So Far So far, the shortest known solution takes 87 turns (9 turns from optimal), and was found by Retudin. Progress over time: Date Moves Found by 2022-09-29 87 Retudin (initial) 97 ...
stewartIM's user avatar
  • 246
8 votes
1 answer
492 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: ...
ultimate's user avatar
  • 183
5 votes
1 answer
633 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)...
Bernardo Recamán Santos's user avatar
40 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 ...
Florian F's user avatar
  • 29.8k
17 votes
2 answers
1k 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 ...
Edward H's user avatar
  • 1,058
4 votes
2 answers
2k 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-...
JHB's user avatar
  • 89
3 votes
1 answer
676 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 ...
JHB's user avatar
  • 89
3 votes
2 answers
446 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 ...
Eric's user avatar
  • 6,498
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 ...
David G.'s user avatar
  • 113

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