Questions tagged [optimization]

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

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11
votes
5answers
2k views

Sorting cards using max 3 stacks

You have a stack of N cards numbered from 1 to N in random order. You want to sort the cards in ascending order using the following procedure: Your initial stack is stack 1. You distribute the cards ...
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 ...
6
votes
1answer
974 views

Frying Three Steaks

You invite your friend to the dinner. so you would like to prepare 3 fried steaks but you do not have much time to cook. You are trying to figure out how to cook all steaks perfectly (fried and ...
11
votes
6answers
753 views

Lots of Gold Stacks and a Balance Scale

You are given X amount of stacks of golden coins, each stack consisting of ten (10) golden coins and a digital balance scale with perfect precision that shows how much difference between weights you ...
7
votes
3answers
565 views

What is the minimum number of steps to solve this cloning particles on chessboard puzzle?

I'm creating a puzzle based on the idea from this numberphile video: pebbling a chessboard. You can see a working (yet unfinished) version here. I would like to give the user a feedback of how well ...
5
votes
2answers
889 views

Largest cages Killer Sudoku

Task 1: Find the maximum value of $n$ for which it is possible to create a regular uniquely-solvable Killer Sudoku (9x9) such that every cage has atleast $n$ cells in it. Rules for killer sudoku ...
2
votes
3answers
381 views

Optimal path around a variable-position wall [closed]

This is a harder version of the fixed wall variation. Every day you walk across a flat plane from a point $A$ to a point $B$. The points are $3$ miles apart. However, every day there is a 50% ...
14
votes
5answers
2k views

Three riders, two horses

We have three riders which need to travel some distance (say, 13.5km) through a rough terrain (no running, no skiing etc., only walking or horse trot), but they have only two horses. The speed of a ...
8
votes
4answers
2k views

Use a circuit to multiply two resistances

Given two resistors of unknown resistances and an infinite supply of wires and other resistors, create a circuit using multiple series and parallel combinations such that the effective resistance of ...
13
votes
1answer
398 views

Inequality with strange equality conditions

Question: For positive real numbers $a,b,c$ and $d$, find the smallest possible value of the following expression: $$\large{\left \lfloor{\frac{b+c+d}{a}} \right \rfloor+ \left \lfloor{\frac{a+c+d}{...
9
votes
1answer
1k views

Ernie and the Geometric Ginger Cookies

Ernie loves cooking and it's always worth the wait as he follows his curiously precise recipe to make Ginger Crunch Cookies. So I was happy to drop around when he invited me to help test his latest ...
2
votes
1answer
187 views

The first trip to the planet Nars

MASA have built a rocket to fly to the planet Nars which contains millions of tons of fuel which the Earth has run short of. The planet is 100 light-years away from earth. MASA has enough fuel to ...
3
votes
4answers
1k views

Sell the fuel and become a Millionaire [duplicate]

You are living in the 22nd century. The fuel prices are unimaginably high and it is very rare to get, so the Government has introduced some new laws to control fuel smuggling. Rule 1: One cannot ...
4
votes
1answer
433 views

Tune a podracer and choose the pilots by solving the podracer tuning equation

A long time ago, in a galaxy far, far away... These are troublesome times: The Galactic Republic is gone, the Jedis were exterminated due to order 66, Vader and Palpatine rules the galaxy with ...
2
votes
1answer
202 views

Is this two-sliding-block overlapped puzzle equivalent to the 8-puzzle?

I'm creating a new puzzle: two sliding blocks 8-puzzle, one on top of the other. Several pieces are covered and cannot be moved until the covering piece moves away. The objective is to pair colors, no ...
20
votes
3answers
677 views

Concentrating tokens on an infinite board

One token is placed on each square of an infinite checkerboard. One square is marked with an X. You want to get as many tokens on the marked square as possible. To do this, you may make any finite ...
13
votes
3answers
813 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 ...
3
votes
1answer
287 views

The lost drone at the Great Wall of China

Inspired by Blindfolded and disoriented near the Great Wall of China A drone is stationary at a spatial point about 1 m from the Great Wall, which is a vertical plane rectangle with height 5 m and ...
12
votes
7answers
3k views

Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
2
votes
3answers
1k views

Folding a hexagon to a rectangle or square, with uniform overlap

A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a fold correspond to folding some fabric along a straight line, without ...
2
votes
2answers
316 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, ...
5
votes
2answers
620 views

Find multiple dishonest people

Recently I travelled far distance by train and a stranger told me this riddle but I never got the answer: 100 years ago, when far distance travelling was something special, a traveller came back from ...
7
votes
1answer
406 views

Shortest time interval measurable via burning a rope

You are given some matches, a rope, and a pair of scissors. The rope burns irregularly and takes 60 minutes to burn end to end; however, we know that the burn rate at distance $x$ from the left end is ...
4
votes
3answers
268 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
630 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
402 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 ...
7
votes
4answers
756 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 ...
2
votes
1answer
300 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
399 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
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 ...
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 ...
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 ...
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 ...
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 ...
9
votes
2answers
643 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 ...
4
votes
2answers
516 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 ...
5
votes
1answer
943 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 ...
6
votes
3answers
401 views

Abalone Migration

Abalone is a 2-player board game. Here's a brief explanation from Wikipedia: The board consists of 61 circular spaces arranged in a hexagon, five on a side. Each player has 14 marbles that rest in ...
-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
297 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 ...
3
votes
0answers
126 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
189 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
498 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 (...
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 ...
6
votes
1answer
484 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 ...
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 ...
5
votes
4answers
645 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,...
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 ...