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.
742
questions
4
votes
2
answers
265
views
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 ...
- 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 ...
- 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 ...
- 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 ...
- 559
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 ...
- 627
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 ...
- 161
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 ...
- 93
1
vote
1
answer
180
views
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 $...
- 31.7k
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 ...
- 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 ...
- 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 ...
- 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 ...
- 31.7k
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&...
- 31.7k
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 ...
- 8,223
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 ...
- 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 ...
- 1,015
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 ...
- 689
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 ...
- 689
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 ...
- 669
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 ...
- 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 ...
- 574
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 ...
- 31.7k
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 ...
- 8,223
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 ...
- 627
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 ...
- 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!...
- 8,223
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 ...
- 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). ...
- 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 ...
- 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:...
- 627
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 ...
- 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-...
- 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 ...
- 8,223
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 ...
- 31.7k
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 ...
- 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, ...
- 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 ...
- 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 ...
- 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
...
- 31.7k
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 ...
- 31.7k
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 ...
- 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 ...
- 16.8k
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 ...
- 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 ...
- 2,699
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 ...
- 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 ...
- 2,699
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 ...
- 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 ...
- 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.
- 31.7k