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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4 votes
2 answers
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Waffleing my Egg

This morning I had a waffle and a fried egg for breakfast. The fried egg was cooked with a mold, so it was perfectly round and three inches in diameter. The waffle was a 3-inch by 4-inch grid of one ...
DqwertyC's user avatar
  • 7,899
6 votes
5 answers
466 views

Minimum K for detecting fake pearls in one weighing

There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and the number ...
Pumbaa's user avatar
  • 802
126 votes
5 answers
140k views

Is this duplo train track under too much tension?

My kids were making this train track of duplo the other day, and this is what they put together. They are still very young, and for them, this is something big. They were really proud that they ...
Lezzup's user avatar
  • 4,914
-4 votes
1 answer
159 views

Find the Rat in the Hole

A rat is in one of 100 holes that are in a line. Each night he moves to the left or right 0,1, or 2 holes randomly selected. You pick one hole each day to look in until you find him. What procedure ...
Bob Bixler's user avatar
13 votes
2 answers
453 views

Minimum lines needed to draw the 12 pentominoes

You need 4 lines to draw the monomino and the same for the domino You can draw the 2 trominoes with 7 lines For the five tetrominoes I could do it first with 16 lines Then 15 lines And my best try ...
Rodolfo Kurchan's user avatar
0 votes
0 answers
73 views

Find the largest number with unique digits, that is divisible by each of its digits [duplicate]

Find the largest number with unique digits, that is divisible by each of its digits. For example 132 has unique digits and is divisible by 1, 2 and 3. But it is not the largest such number. Can you ...
Teodor Dyakov's user avatar
9 votes
2 answers
633 views

Pay each amount with at most two coins

Euro cent coins come in the denominations 1, 2, 5, 10, 20 and 50 cents. You are inconvenienced by the fact that you need a lot of coins to pay each amount up to 100 cents. To pay 99 cents, you need 6 ...
Tilman's user avatar
  • 93
1 vote
1 answer
180 views

Visiting all strings by swapping

Consider the following strings ...
Simd's user avatar
  • 6,627
7 votes
1 answer
359 views

Prime Twelve Apostles

You are given an empty square grid. Each cell can be an island with a positive integer $n$ or a bridge connecting islands. The following rules apply: Each island with a number $n$ must have exactly $...
Dmitry Kamenetsky's user avatar
5 votes
1 answer
316 views

Maximize "sudoku" occurrences in a sudoku

How often at most can "Sudoku" occur in a valid (9x9) sudoku? create a valid sudoku replace (all occurrences of) 5 of the numbers by the 5 letters in "sudoku". (and leave the ...
Retudin's user avatar
  • 7,619
11 votes
6 answers
2k views

The shorter the message, the larger the prize (version II)

This is a successor question to The shorter the message, the larger the prize . For completeness I will include the entire question even though only the numbers have changed. Solutions to this puzzle ...
Simd's user avatar
  • 6,627
14 votes
1 answer
1k views

The shorter the message, the larger the prize

Andrei and Belle have been set a task by their “friend”, Carroll. Carroll has promised them money depending on how well they do. Carroll will give a 99 bit array to Andrei and a different one to ...
Simd's user avatar
  • 6,627
5 votes
2 answers
570 views

Largest binary rectangle without any arithmetic progressions

What is the largest rectangular grid (by area) that you can color in red and blue such that there is no red cell halfway between two red cells and no blue cell halfway between two blue cells, moving ...
Dmitry Kamenetsky's user avatar
3 votes
1 answer
212 views

A special binary string

I was inspired by this puzzle. What is the longest binary string of "0" and "1" you can form such that no "0" is halfway between two other "0" and no "1&...
Dmitry Kamenetsky's user avatar
3 votes
1 answer
163 views

Lowest possible ratio of number of borders to countries annexable

There's been a recent trend on Reddit of finding how many countries can be colored in by: Coloring nation a. Coloring b nations, those touching a's borders. Coloring c nations, those touching b's ...
Rewan Demontay's user avatar
5 votes
1 answer
325 views

Nuts and screws

Imagine that you are given a box with n nuts and n screws. Each screw have different size (diameter) and on each screw there is ...
popcorn's user avatar
  • 263
2 votes
0 answers
140 views

Trippples - optimisation [closed]

Trippples Introduction Tripples (BGG) is a board game from the 1970s. It is played on an 8x8 grid, and each tile on that grid (except the corner starting tiles, and four blank tiles) contain three ...
simonalexander2005's user avatar
11 votes
5 answers
2k views

Green Triangles Puzzle

This question is closely related to Green Hexagons Puzzle. Start by choosing some triangles to be green. If a triangle is sharing an edge with at least 2 green triangles, it becomes green. This ...
PuzzleAndy's user avatar
7 votes
2 answers
1k views

Green Hexagons Puzzle

Start by choosing some hexagons to be green. If a hexagon is touching at least 3 green hexagons, it becomes green. This repeats for as long as possible. What's the minimal number of initial green ...
PuzzleAndy's user avatar
1 vote
3 answers
419 views

The secretary problem goes on budget

Secretary problem describes a scenario where a company wants to hire the best secretary from sequential interviews of candidates that can be done only once. In budget secretary problem a company has ...
10010100102ohno's user avatar
6 votes
1 answer
654 views

Cable with mixed wires

Let's say you have a cable that has n wires. Each wire on the left side corresponds to one wire on the right side. However you cannot distinguish between the wires ...
popcorn's user avatar
  • 263
12 votes
3 answers
4k views

I Hate Traffic And So Do You

I need to travel through the city from my house to school, but the traffic is horrible right now. I can only move along the city's grid with the following conditions: • blocks with traffic (marked in ...
RonnieChen's user avatar
8 votes
3 answers
591 views

Cutting a square into integer triangles

You are given a square piece of paper with size 10x10 units. What is the most number of triangles that can be cut from this square, such that: Each triangle has integer sides. Each triangle is ...
Dmitry Kamenetsky's user avatar
6 votes
2 answers
275 views

Kingly Laziness

What is the minimum effort the White king must put into arriving at this destination? His Majesty is not feeling productive today. This position was composed by Gianni Donati and published in Phénix ...
Rewan Demontay's user avatar
1 vote
2 answers
219 views

Put ABCDE and ABCDEF words combinations in squares

I can put the 6 combinations of ABC words in a 3x3 square ABC = 3 letters = 6 combinations in a 3x3 square For ABCD = 4 letters = 24 combinations in three 4x4 squares a solution was found by George ...
Rodolfo Kurchan's user avatar
5 votes
2 answers
1k views

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
  • 4,641
1 vote
0 answers
167 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
514 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
  • 18.2k
6 votes
4 answers
721 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
  • 802
8 votes
4 answers
877 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
  • 1,038
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
  • 1,802
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
3 votes
2 answers
319 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
701 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
  • 1,038
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
  • 13.4k
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
  • 4,843
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
1k 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
347 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
  • 21.8k
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
211 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
  • 601
4 votes
1 answer
242 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
394 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
  • 601
3 votes
2 answers
220 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
414 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
  • 30.2k
3 votes
1 answer
310 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
  • 30.2k
-4 votes
2 answers
138 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

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