Questions tagged [optimization]

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

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-5
votes
3answers
197 views

How can one reliably prevent pedestrian access to a parking garage, but allow vehicular access? [closed]

Consider a typical private parking garage for a condominium or apartment building. There is currently a typical garage gate that opens and closes (slowly) to allow vehicles to pass safely through the ...
11
votes
6answers
11k views

1 Fake Coin among N Amount of coins

You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale. You are asked to find the fake coin in totally 5 times weighing on the Pan ...
19
votes
8answers
2k views

30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
8
votes
3answers
395 views

Find a straight tunnel 2

You have the same plugging task as in Find a straight tunnel , but now the problem requires a bit more imagination: Bob has a field, which is a regular polygon with $N$ sides and perimeter $P$. ...
15
votes
3answers
2k views

6 Water Glasses Upside Down

There are 6 water glasses as shown in the picture below: You need to turn all of them upside down with the rules below: You have to choose any 5 of them at every turn. Chosen ones need to be turned ...
-4
votes
3answers
288 views

What's In Your Pocket?

You have in your pocket a set of U.S. coins.1 Using these coins you can count out a face-value total2 of exactly $96¢$, $97¢$, $98¢$, or $99¢$, using exactly the minimum number of coins possible for ...
11
votes
3answers
833 views

16 Two Colored Line up v2

This is the follow-up question for 16 Two Colored Line Up This time, you are not supposed to solve it, but find the worst possible arrangement for each square, which will make the number of steps ...
8
votes
2answers
366 views

16 Two Colored Line up

We have a different type of puzzle which consists of 4x4 board with numbers on it; Your task is to put numbers in the correct order as given in the diagram above. In each step, you can take one ...
32
votes
6answers
6k views

Will a greedy algorithm solve Tatham's Flood?

I was just investigating some of the puzzles on Simon Tatham's website, and came across Flood, in which we start with an $n\times n$ grid of cells each of which is filled with one of $k$ predetermined ...
9
votes
4answers
1k views

The Universe and Spaceships

It is given that there are infinite planets in the universe and every planet has exactly one spaceship on it. (Thus there are infinite spaceships too.) The distance between planets is unknown. As ...
6
votes
2answers
563 views

A Number Game for your Soul

The devil has suggested a deal to you. You play a game with him, if you win you go to heaven when you die, if you lose you go to hell. Thinking you can beat him, you take him up on the offer. Here is ...
7
votes
3answers
460 views

Minimum money needed for the worst case to guess the right number

You are going to guess a number from $0$ to $100$. If your guess is smaller, you are told and you need to pay $x$; if your guess is larger, you are told and you need to pay $y$. The game stops when ...
8
votes
1answer
434 views

A perfect metro map

You are working for a company and asked to create a perfect metro map where there will be as many stops as possible. But there are two constraints which limits the number of tracks (railroads) and ...
13
votes
1answer
1k views

What is the optimal first move in Mastermind?

For a given number of positions/holes and a given number of colors, which initial guess eliminates the most possibilities for the solution at a minimum? For 4 positions, it's AABB. What is it for 5, ...
7
votes
4answers
361 views

No Square Allowed

On a Chessboard, place as many chess pieces as you can. Position the center of each piece on the center of a square. Avoid placing any 4 pieces at the corners of a square (even a tilted square). ...
9
votes
8answers
3k views

Puzzle similar to 15-puzzle but more moveable pieces?

In the name of Science!™, I'm trying to look for (or, in the worst case, create) a puzzle/game similar to the n-puzzle whereby a player or player(s) have to put some pieces in a particular order (e.g. ...
3
votes
4answers
266 views

Trash Bin Factory

Trash bins are to be fabricated from $4ft.$ x $8ft.$ Ga.#16 Aluminum sheets. To produce $1$ bin, it will take some cutting, bending and welding of a single Aluminum sheet. To maximize the ...
9
votes
3answers
278 views

The Flea Circuit

Starting on a square of the checkerboard, "The Flea" is trained to jump to the center of another square. Then it keeps jumping (center to center) from square to square all around the board. It is ...
5
votes
2answers
574 views

Hnefatafl - a lost Art

Hnefatafl (Ner-far-taff-all) is a Tafl Game, though it is a lost art in the modern day. The aim of the game is either to capture the king, or get the king to a corner depending on which side you are ...
-5
votes
5answers
343 views

Access Road System (Formerly Path of the Rat)

There are six towns (see map below) that needs a road system to have access with each other. What is the minimum total length of 10ft. wide road pavement that can be constructed? o---1mile---o---...
3
votes
2answers
447 views

Get the largest number using the crazy circuit board

There is a crazy circuit board with three kinds of elements which can change the signal value. All intersecting paths are connected (but paths touching by a single point are disconnected). There is ...
2
votes
2answers
146 views

Play against all other team members

Situation There are 5 teams, assume they have 10 members per team. Objective Together, the members of each team should be matched pairwise with all opponents in the minimum number of rounds. So, ...
5
votes
3answers
306 views

Minimum steps on a numberline

Given an infinite numberline, you start at zero. On every i'th move you can either move i places to the right, or i places to the left. How, in general, would you calculate the minimum number of moves ...
8
votes
2answers
733 views

Lots of Gold Golden Coins and a Scale

Following my previous question: Lots of Gold Stacks and a Balance Scale You are given 10 stacks, each stack consisting of N golden 10g-coins and a digital scale with perfect precision that shows ...
-3
votes
1answer
213 views

Shortest path to the middle [closed]

You are in the desert. You are instructed to get to the middle point between to visible marks far from you (meaning you can see them - see the direction to them - but you do not know how far are they ...
0
votes
2answers
281 views

How can 32 teams rotate through 8 games without overlaps? [closed]

So I have to arrange a rotation schedule for a tournament. We're aiming for 32 teams. There will be 8 stations and 4 teams competing simultaneously at each station. We want all 32 teams to hit each ...
4
votes
1answer
344 views

Can I Haz My Eye Center'd 2?

I have noticed Can I Haz My Eye Center'd? puzzle, which I know in slightly different formulation: You have a disk on a table and a point A on it. You need to cut the disk into smallest possible ...
16
votes
5answers
811 views

Maximize the number of paths

You have exactly 990 edges. Assemble them into a simple undirected graph with two distinguished vertices A and B, such that the number of different simple paths from A to B is as large as you can make ...
2
votes
2answers
725 views

Can you help me understanding the Stones game?

I am trying to understand the Stones game stated here. The stones game is a simple game, it is also a very old game which is unknown to almost everyone. The game starts with N stones and M ...
7
votes
1answer
293 views

Least amount of moves is required

You have 8x8 board and 9 identical pieces placed in a 3x3 square at the bottom left corner of the board. You are going to play a very simple game. Your task is to move these 9 pieces to the 3x3 square ...
1
vote
2answers
381 views

Off roading in a desert [closed]

You’re off-road, in the desert, driving an all-terrain vehicle. You’re $10$ miles off the straight highway, and your destination is $100$ miles ahead, also $10$ miles off the straight highway. You can ...
-3
votes
4answers
635 views

Variation of 1000 bottles of wine puzzle

So I came up with a variation of the famous problem https://www.reddit.com/r/math/comments/3o0mfi/a_king_1000_bottles_of_wine_10_prisoners_and_a/ There are n ...
9
votes
3answers
738 views

What is the 'best' way to tilt through a D20?

A regular D20 die (icosahedron) as depicted above has the number 1 to 20 arranged on its faces such that the sum of opposing faces is 21. Each triangular face touches three other faces directly by a ...
9
votes
2answers
381 views

Third timer's a charm

Three motorized 24-hour light timers are arranged between a power outlet and a light bulb, with timer A parallel to a daisy chain of timers B and  C. For these timers, devise schedules that ...
6
votes
1answer
980 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
793 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
592 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 ...
2
votes
3answers
387 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% ...
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 ...
14
votes
5answers
3k 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 ...
2
votes
1answer
203 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 ...
13
votes
1answer
417 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}{...
2
votes
1answer
223 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 ...
5
votes
1answer
454 views

Optimize cloth usage

A factory that manufactures clothing cuts multiple garments at once. Sometimes a number of markers are used for a job. Each marker may have a single size or multiple sizes depending on what is needed....
20
votes
3answers
692 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 ...
12
votes
3answers
955 views

Day and night of the two timers

            Make a non - 24 - hour day /  night cycle       &...
11
votes
1answer
576 views

Blindfolded and disoriented near a space station

Following on from the recent blindfolded near the great Wall of China puzzle. Suppose you are floating in space a mile away from a huge space station (the death star perhaps). Assume that the death ...
3
votes
1answer
293 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 ...
8
votes
3answers
766 views

Odd hours with two timers

Two motorized 24-hour light timers are daisy chained between a power outlet and a light bulb. For these timers, devise schedules and choose initial times that produce the following repeated 9-hour ...
8
votes
3answers
572 views

Halve time with two timers

Two motorized 24-hour light timers are daisy chained between a power outlet and a light bulb. For these timers, devise schedules and choose initial times that produce the following repeated lighting ...

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