# Questions tagged [optimization]

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

270 questions
Filter by
Sorted by
Tagged with
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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% ...
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 ...
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 ...
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}{...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...