Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

Questions tagged [optimization]

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

Filter by
Sorted by
Tagged with
4
votes
3answers
273 views

The Witch Invites

Halloween is just around the corner and the witch is planning a little party for the 100 villagers of the nearby village. Since the villagers burned down her house again and again during the last few ...
3
votes
1answer
636 views

Clock values using only the digit 3

What is the minimal number of 3s required to create a clock where each of the hours is replaced by a mathemetical expression using only the digit 3 and standard mathematical operators? A friend ...
11
votes
1answer
403 views

What is the smallest rectangle containing the squares of 1 through 100?

Let us suppose that we have an $m\times n$ grid such that every element is a digit in base $10$. Then we can read the numbers from a grid such that we fix a starting element and go to one of the eight ...
2
votes
1answer
301 views

Registers in Infinityland

In Infinityland, people have mastered full control over Infinity. They have built registers which are capable of holding as much data as needed. There are two types of registers in infinityland which ...
6
votes
3answers
402 views

Five-hand poker

Both players are dealt $26$ cards from a regular $52$ card deck. He discards $1$ and makes $5$ hands (from the remaining $25$) in any order, each with $5$ cards. His score is given by the sum of ...
7
votes
4answers
758 views

Born to lie, to live, to die

There is a race which has a truth gene. It consists of 3 alleles, namely T, F and O. A person inherits one allele from each of his parents, hence he/she has always exactly two alleles. For example, if ...
7
votes
1answer
565 views

This ant sure is smart. But how fast is it?

A mad scientist uses ethically questionable methods to study the spatial cognition of ants. Last time, he left his lab ant in a cubic room and filled it with painfully intoxicating gas, capable of ...
2
votes
2answers
317 views

Closing taps (generalisation) [closed]

You have a tanker that can hold any amount of water. You have $n$ taps that either let in or let out water. The rate of flow of water (in $ml/min$) for each tap is given by $f_n$ (positive for inflow, ...
2
votes
1answer
155 views

The incredible polyhedron

Based on The Erasmus polyhedron by @Gamow.. Construct a 3D convex polyhedron of any single material that can float in water such that $x\%$ of its volume is below water level and $y\%$ of its ...
10
votes
3answers
589 views

Find the fastest path through this Brazilian concretist poem

One day, a small jet was flying over the concretist poem "Velocidade" (Speed), by the Brazilian poet Ronaldo Azeredo. In order to cover every vowel present in this poem, it goes in straight line from ...
9
votes
2answers
647 views

$100 + n$ boxes for the king!

There are 100 friends and $n$ enemies in a room. In the next room, there are $100+n$ open boxes, and $100+n$ keys, one corresponding to each box. They are numbered for easy identification. A box can ...
5
votes
1answer
957 views

Generalisation of cup riddle

I'm asking for a generalisation of this question. There is an $m$ sided board with $m$ cups. Some of the glasses are facing upwards and some upside-down. Your goal is to arrange the glasses so that ...
12
votes
3answers
2k views

Cracking a combination lock

Let's consider the humble mechanical combination lock. The basic type has $n$ dials, with $k$ digits on each dial, for a total of $k^n$ possible combinations. (Typical luggage locks or suitcase lock ...
4
votes
3answers
438 views

Least amount of trips

There are two rooms. One room contains ten switches, and the other contains ten lights. Each switch controls one light, and no two switches control the same light. It is not known which switch ...
4
votes
2answers
521 views

Lock Optimisation

In a simple combination lock, a sequence of several digits is used as a password, with one wheel per digit. Generally, it is not possible to unlock the lock without knowing the password, but due to ...
-4
votes
2answers
176 views

The smallest compression [closed]

What is the most compact way to store the sentence The quick brown fox jumps over the lazy dog without losing data? Whatever way you think of must be explained and ...
5
votes
2answers
299 views

Paying an unusual toll to the troll

You approach a bridge and see a troll. He throws down finite $n>0$ bags. Each bag, $B_i$, contain 1 or more of 4 possible buttons. $B_i$ contains $S_i \subseteq \{green, red, blue, yellow\} \land ...
19
votes
4answers
2k views

How many boxes are conductors?

The Question (Some knowledge of potential difference, resistor combinations, etc. required) You have 1000 boxes. Some (or none) of them are conductors (of negligible resistance). The rest are ...
3
votes
0answers
129 views

Minimum number of telephone calls needed to exchange information [duplicate]

There are 16 secret agents who each know a different piece of secret information. They can telephone each other and exchange all the information they know. After the telephone call, they both know ...
6
votes
1answer
190 views

Social Network Messaging Problem

Brady and Sarah have been messaging on a site for a while now. The site tells you when you sent your messages; but not in exact detail. For example, Sarah messaged Brady "What's up?" 2 hours and 31 ...
6
votes
1answer
487 views

Capture The Stones

This puzzle was created by me as a single-player variation on the game of go. The objective here is simple: capture all 41 grey stones on the board below in the least number of moves. Just like in ...
6
votes
1answer
503 views

Mastermind - all but last attempt

This a variation of the traditional game mastermind. There are 4 pegs and 6 colors of pegs in the code (repeats allowed). All rules are as usual, except for this one: You are not given any hints (...
16
votes
3answers
2k views

Bulls without cows: how many steps are needed to solve this?

I'm bad at this sort of minimum-solve problems so I'm asking for you, proud riddle solvers! There's this huge hangar with 72 different airplanes. They come in six different colors Each color has ...
22
votes
7answers
2k views

How much water do you need to cross the desert?

This question is inspired by Terry Pratchett's "Small Gods," in which an army crosses a vast desert by making multiple trips and caching water along the way. 1. Provide an answer. 2. I doubt I'm the ...
4
votes
5answers
17k views

How can the animals get across the river without a fight breaking out?

There are three dogs and three cats that have to be transported across a river: a big dog, a medium dog and a small dog, a big cat, a medium cat, and a small cat. Rules: The raft can carry two ...
9
votes
1answer
604 views

Building a cheap road

The governor of Reniets (a land far, far away!) is known to be very stingy. He has to build a road which connects all the five cities in the region, which are oddly arranged on the vertices of a ...
1
vote
1answer
245 views

Find the optimal dot configuration

Rules: You have 9 dots, labeled A through I. You choose a layout (arrangement) for the 9 dots. You must connect the 9 dots with straight lines (no curves or extra lines). The object is to ...
10
votes
5answers
817 views

Houses in a grid

You are a city planner tasked with the placement of unit-square-sized houses in a rectangular-grid allotment, the size of which is up to you but must be as small as possible to save money. The number ...
19
votes
6answers
3k views

Trapped in my Cellar

I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
1
vote
1answer
469 views

Slot Machine Challenge

Karen owns a restaurant/bar. She wants to attract more customers, and is building her own custom slot machine game, which she can use to give away free drinks or prizes. The more a customer spends, ...
2
votes
2answers
228 views

Is there a better solution to parallel segments problem?

There is a puzzle: Find a finite set of points with the following property: 1. Points are placed in space (not on a single plane) 2. If you take any pair of points A and B there are different ...
2
votes
1answer
205 views

Shutting down all lamps [closed]

I found this problem from http://artofproblemsolving.com/community/c163h564755p3301930 . I have $n=2017$ lamps in a circle, and enumerated by $L_1,\ldots,L_n$. Some of them are switched on and some ...
3
votes
4answers
724 views

Another poisoned bottle question!

There are $1000$ bottles of wine, of which $n\leq10$ are poisoned at random. (You don't know the exact number) A person consuming the poison dies on the midnight of that day. You have $2$ prisoners ...
4
votes
5answers
1k views

The game of Sevens

There is a popular game, named Four fours, where you have to find the shortest mathematical expression for every number from $1$ to $n$, using only the number $4$ and some operators. My variant of ...
2
votes
2answers
3k views

The case of the 4 campers and the rickety bridge! [duplicate]

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough battery left for seventeen minutes. The bridge ...
-1
votes
3answers
303 views

Extremely hard prime factor based true-false statements [closed]

Let us suppose there are $n$ statements on the list. Each statement may be true or false. The first statement declares: I am true. Therefore, it could be true, or it could be false. After this, ...
7
votes
4answers
1k views

Minimum cells to fill grid without consecutive neighbours

Imagine you have a m x n grid which is initially colored white. you can fill in a cell with black color if and only if there are no immediately neighboring black cells (no black cells to the left/...
6
votes
5answers
2k views

How to maximize your wages?

You're trying to work out how to maximize the wages you receive in the month of February (in a non-leap year). You must work at least 5 days a week and at least 5 hours a day, but you can also work on ...
53
votes
8answers
5k views

Find a straight tunnel

There is a circular area with radius 1 km. And there is a tunnel, which is just under the surface, but invisible - unless you dig. It is known that the tunnel goes under the area (at least touches it ...
37
votes
11answers
4k views

Sudoku net that is always solvable

A sudoku net is a 9x9 grid where every cell is either (blank) or has a cross (block). A random solved sudoku is chosen. The net is placed on top of the sudoku (in any of the 4 ways). We can only see ...
5
votes
4answers
648 views

A tour of 36 cities

Each of 4 people is touring 36 cities separately. Each of the 36 squares in the illustration below represents a city. To make the answers shorter, each city has been given a 1-character name, from A-Z,...
9
votes
3answers
3k views

$n$ couples crossing a river

There are $n$ couples on one side of the river. Nobody is on the other side. They have a boat that accommodates up to 2 people. For every trip across, someone(s) must bring the boat back as well. The ...
4
votes
3answers
412 views

$n$ monsters and $n$ people

There are $n$ monsters (M) and $n$ people (P) on the left side of a river. Nobody is on the right. They have a boat that can hold up to 2 beings. At no point on time may either of these be true: $$M_{...
2
votes
8answers
199 views

Pass the Baton competition 6 members teams

The following diagram depicts a Pass the Baton tournament (Note: due to a merge, some of the answers below use this image instead.) Each team consists of 6 members, 2 at the central point $E$, and ...
7
votes
3answers
813 views

Can you create a Minesweeper puzzle with 'information crossover'?

The object of this puzzle is to construct a Minesweeper grid with a special property. The grid can be any shape, but it must have four labeled squares around the outer edge. Like this: The four ...
9
votes
1answer
610 views

Maximize 'chains' in a Sudoku

Yet to be solved. Take 2 numbers such that $N, M \in \{1,2,3,4,5,6,7,8,9\}; N \ne M$. Start with a solved 9x9 Sudoku grid. Find any $N_1 = N$. Find an $M_1 = M$, in the same row as $N_1$. In the ...
11
votes
1answer
535 views

Bouncing Robots: Graphical Puzzle [closed]

Robots are indicated by the arrowhead shapes and the labels "r", "y", "b", "g". The label obviously corresponds to their color. The aim of the puzzle is to pick up the shapes and put them down in the ...
16
votes
8answers
2k views

Rigged casino that prevents pairs

This question is still active as the answer from @Sleafar has just arrived. Not yet solved. Scenario The heads of 3 top terrorist organisations are planning to play an extremely high-stake poker ...
13
votes
3answers
819 views

Searching for a secret door

You have reached the final stage of a game show, and now face an endless row of doors labelled $\ldots,-3,-2,-1,0,1, 2, 3,\ldots$, going from minus infinity to plus infinity. Your goal is to detect a ...