Questions tagged [optimization]

A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).

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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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 ...

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