Questions tagged [optimization]
A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
310
questions
4
votes
1answer
87 views
Maximum number of legal moves after n moves in a chess game [closed]
Given the chess start position :
What is the maximum number of legal moves white can play after $n$ full moves?
We will assume black is helping white in this task.
I want the best answer you could ...
1
vote
1answer
126 views
The Big Cube and Squares Puzzle
The following logical puzzle is mainly inspired by a mathematical contest I went to.
Part A
You are given a cube. How many planes cross this cube by at least 3 vertices? This number will be named $...
7
votes
1answer
124 views
What is the minimum-value piece combination necessary to checkmate in this game of Crazyhouse?
Imagine you're playing a game of crazyhouse, which operates like standard chess, except that you have a pocket of captured pieces that you can drop on the board in any legal location as your move.
...
7
votes
3answers
146 views
Placing The Black King
In this position, White’s sole aim is to castle. But in order to do so, they must promote their pawn to a queen to force a Black bishop move. The 10 black kings represent where Black’s king can safely ...
7
votes
3answers
407 views
What is the minimum count of steps required to complete this maze correctly?
Here's a map:
How to play
Legend:
B = Boost
X = Objective
(•) = ...
1
vote
1answer
59 views
k-threats Chinese Cannons Chess: Part 2
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
4
votes
1answer
67 views
k-threats Chinese Cannons Chess: Part 1
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
10
votes
3answers
501 views
Pieces of paper without consecutivity condition
TL;DR: like this puzzle but with an arbitrary number of papers and without the condition that the papers chosen must be consecutive.
You are given $n$ pieces of paper, and you write down $n$ distinct ...
6
votes
1answer
87 views
Freedom of many choices
There are 40 possible move options for both White and Black players in the starting position. The 4 knights and 16 pawns all have 2 options.
If all the pieces are still on the chessboard, how would ...
7
votes
4answers
312 views
3 Colors of Chess Pieces Attacking Each Other Once Each
Yes, it's another "Chess Pieces Attacking Each Other" puzzle. This time we have 3 colors. Your goal is to place as many of the same type of chess piece (excluding pawns since you can't define the "...
1
vote
2answers
102 views
How can you find the maximum number of cubes when their faces are subsequently painted and placed in a box?
I'm not sure exactly how to visualize this riddle. Can someone help me?. It goes as this:
Mike has many identical cubes whose faces are white. He decides to
take one of those cubes and places it ...
6
votes
1answer
124 views
Most moves by Most number of Pieces
Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces ...
2
votes
1answer
87 views
Footmen And Friends #3: Eviction
Welcome to Episode 3, where we have a strange puzzle for today. Pawns aren't legally allowed on the first and eighth ranks, but today we make an exception for the sake of creating another long but fun ...
2
votes
1answer
72 views
Electrical Roughing-ins
The 27 junction boxes at the ends of electrical conduits must all have a green and red wire taps for the lighting fixtures. Only one wire fits the conduits for safety. The wires should be connected on ...
1
vote
2answers
85 views
How can I find the total number of rabbits if they reproduce at a constant rate? [closed]
The problem is as follows:
Roger adopts two female rabbits and two male rabbits. Three months
later each female rabbit gives birth three female rabbits and three
male rabbits. Assuming that if ...
2
votes
1answer
90 views
Footmen And Friends #2: Leapfrog
Seeing as the pilot episode was a major success, with an outstanding and correct response from one of our viewers, it’s time for Episode 2. Remember, we show puzzles with kings and pawns only! Those ...
3
votes
3answers
201 views
Does there exist a way to find the least number of trials when a certain weight is requested?
I'm not very sure how to tackle this sort of problem:
It is as follows:
At a groceries store there is a two pan scale and two weighs which are
of $250\,g$ and the other of $500\,g$. It is known ...
4
votes
1answer
160 views
Footmen And Friends #1: A Long Ways Away
Tonight premiers the first show of Footmen And Friends, a show dedicated exclusively to kings and pawns. Let's give these soul-men of chess a chance to shine instead of their big sisters and brothers!
...
7
votes
1answer
102 views
What is the minimum-sized Blokus board which can contain all pieces?
Rules:
Each player has the twelve pentominoes, five tetrominoes, two trominoes, one domino, and lone square. These may be flipped and rotated in any manner.
The board on which these are to be placed ...
11
votes
3answers
1k views
How many chess pieces do we have to put at least?
In a $8\times8$ chessboard, a cell is qualified if an adjacent cell (a cell which is on top, left, below, or right of the cell) excluding itself has a chess piece on it. How many chess pieces do we ...
12
votes
3answers
374 views
Fewest polyominoes to construct digits
What is the fewest polyominoes you need so that any one of the numbers $0$ to $9$ can be constructed?
When constructing, polyominoes may be rotated and flipped, but may not overlap.
Bonus: How few ...
10
votes
3answers
394 views
Ten squares inside a rectangle
You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square
is outside the rectange. The sides of ...
3
votes
1answer
95 views
Ratio between surface and volume of a sphere and a cube
The surface to volume ratio of a sphere with diameter d is given by $\frac{\pi d^2}{\frac{1}{6}\pi d^3} = \frac{6}{d}.$
The surface to volume ratio of a cube with side length d is given by $\frac{6 d^...
2
votes
1answer
133 views
Optimal number of moves in “magnetism” puzzle? [duplicate]
Once, I saw a puzzle on Puzzlopia (now a Chinese website, just put a .com in the bold text). I call this "Magnetism", where the board and rules are:
Board:
(recreation)
Rules:
1) ...
15
votes
6answers
637 views
A special triple of factors
Using each of the digits 1,2,3,4,5,6,7,8,9 exactly once, create three 3-digit numbers such that their product is a maximum.
15
votes
4answers
805 views
My Mother's Dish Collection
From every trip she makes, my mother brings as a souvenir a well-decorated dish to hang in a wall. She now has a collection of 12 dishes, all disks, of radii 1, 2, 3, ..., 12 inches respectively.
...
2
votes
1answer
209 views
A challenge-find the shortest solution!
I come here with the challenge today-find the shortest solution!
Recently, I set out to created the longest helpmate possible, not caring for legality or duals I have created this monster as a result....
8
votes
2answers
317 views
Can you open a safe with a lengthy complicated combination?
Two cousins were talking about their parents' safes. "They said I can keep my comic books in their safe, if I figure out the right combination, and enter it on the keypad correctly on my first ...
11
votes
5answers
437 views
Crossing the desert
There are explorers that want to go as far in the desert as possible. One explorer can carry water for himself for 10 days. If they would all stick together, they would have enough water to go 5 days ...
6
votes
1answer
229 views
12 Distinct Weights' Sorting
There are 12 balls with all different weights. You want to sort these balls by weight. You have a friend who will help you with the ordering process. In each step, you give any 4 balls to your friend ...
1
vote
2answers
77 views
How many different ways can be read a number without repeating the same digit in an arrangement which resembles a triangle?
The problem is as follows:
The figure from belows shows a triangular arrangement where there is a
set of numbers. The condition is that in each reading you cannot
repeat the same digit and the ...
4
votes
1answer
177 views
A Box of Puzzle Blocks
A cubical box is required to contain a set of wooden blocks (N right parallelepiped solids that fits in without spaces) which have different edges and colors. No two blocks have the same edge linear ...
5
votes
1answer
111 views
How do I find the total sum of the numbers occupying three different regions of a $3 \times 3$ grid?
The problem is as follows:
The following board must be completed with natural numbers from $1$ to $15$ with no repetitions allowed in such a way that the sum of the numbers on each of the three ...
5
votes
4answers
289 views
How do I find the maximum quantity of trees to be chopped in a field given a square?
The problem is as follows:
In a oasis, a lumberjack sees that a group of palm trees has a $7\times 7$ formation making a square as it is shown in the diagram from below. Find the maximum quantity of ...
11
votes
2answers
414 views
Checkmate with two knights, but with a twist
It is well known that two knights and a king alone cannot force a checkmate. But that it on a 64-sqaure board.
According to Edward Winter’s C.N. 5449, William Shinkman found a way to give mate in a ...
1
vote
3answers
110 views
How do I find the least number of times a shuttle can travel from one place to another?
I often see this situation in exams and I'd like to know if there is any kind of algorithm or shortcut that I can use to solve this riddle instead of just guessing or trying to play Where's wally with ...
8
votes
3answers
1k views
30 fake coins out of 99 coins v2
Follow up question to my other question, but totally different methodology required.
You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect ...
4
votes
1answer
161 views
Terrorists transporting Hostages through the desert
You belong to an intelligence agency that is monitoring some terrorists. There are three of them in the Hideout A with three hostages and a bomb. Unfortunately, this hideout is extremely secure. But ...
5
votes
3answers
329 views
land of light bulbs
Leuks is the land of light bulbs, where the bulbs are leading a peaceful life, with no humans at all. Presently there are 100 residents . (Of course, they all are light bulbs!).
Let $a_{1}, a_{2}, . ....
5
votes
3answers
213 views
Rawrdon Mamsay pays a visit
Now, I should warn you, this is one of my practical problems; meaning I don't know the solution and the answer's probably anticlimactic (like this or that). Still...
My old pal Rawrdon Mamsay is soon ...
12
votes
3answers
2k views
Find number 8 with the least number of tries
You and your friend plays a game. In this game, there are numbers written on the cards from 1 to 12 on one side (so 12 cards in total). The other side is blank. You can write anything on the blank ...
2
votes
1answer
119 views
In and out, and back in again
With White to move, how long will it take for both sides to cooperate, i.e. this is a helpmate, and checkmate Black?
This is based on a problem made made by Otto Blathy. And yes, I know that the ...
4
votes
1answer
166 views
Find the least expense?
You want to build a shop between three roads in the shape of an equilateral triangle.
What would be the best location for the shop so that you can reach each road with the minimum transportation ...
17
votes
4answers
3k views
Smallest PRIME containing the first 11 primes as sub-strings
In Smallest number containing the first 11 primes as sub-strings, @Alconja successfully found the smallest number which contains the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31) as ...
6
votes
5answers
220 views
Chess Construction Challenge #3-The Inverse Babson
Another day, another task!
Today's challenge is to construct four positions, with White to move and win, such that:
In each position, White's move is to promote to a particular piece, for a position ...
6
votes
5answers
2k views
Minimum number of lines to draw 111 squares
Find the minimum number of lines to draw 111 squares.
For example, you can draw a single square using 4 lines i.e 2 vertical and 2 horizontal.
Similar, you can draw a 2 square in the grid using 5 ...
0
votes
0answers
93 views
Tales of Two Cities (With no Gas Stations in between) [duplicate]
Two cities A and B are 100 miles apart. A person has to travel from one city to the other in his old old car, which can travel only 50 miles with its tank full. Unfortunately, there are no gas ...
11
votes
2answers
2k views
The economy of trapping
A queen on the center of the board has 27 possible moves. Sometimes a queen can be trapped, like in the position below.
Note: This is just an example of a what a trap should be like-every possible ...
8
votes
2answers
1k views
Dodgy Dies: The Puzzling Premiere
Inspired by the "Treasure Hunter Monolith" minigame from Danganronpa V3
Dodgy Dies Guide
Terminology
Block - a single die on the grid.
Cycle - a list of blocks
Value - the ...
6
votes
1answer
236 views
Don't bully your cousin at Reversi
Title (only) inspired by Don't bully your little sister at chess
Prologue
Well, this happened when I played Reversi with my cousin a few days ago...
I, not being as nice as @Arnold ...
