Questions tagged [optimization]

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

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31
votes
7answers
6k views

Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
73
votes
15answers
80k views

A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
18
votes
3answers
3k views

Knights and jokers

There are $N$ men. $K$ of them are knights, $M$ of them are jokers. $N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd. Knights always tell the truth, ...
11
votes
6answers
12k 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 ...
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 ...
16
votes
4answers
1k 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. ...
20
votes
5answers
809 views

Square Spin #1: Sun and Moon

Defining Square Spin Lets play a game! The aim of this game is to transform one image into another using the least amount of moves possible. Here is what a move consists of: ...
8
votes
3answers
773 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 ...
2
votes
2answers
4k 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 ...
10
votes
1answer
294 views

Barrel - Part 3

An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Title based on this xkcd. This is a continuation of Barrel - Part 1 and Barrel - Part 2, but this puzzle is still self-contained. ...
49
votes
6answers
5k views

Eight coins for the fair king

You are responsible for creating new types of coins for the court. King respects the forgetful: he wants you to create 8 coins of different value, no more. King respects the feeble: he wants that any ...
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 ...
11
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 ...
7
votes
3answers
834 views

Dinosaur Egg Drop v2

This question is a little different and kinda follow-up version of Dinosaur Egg Drop 1- You have 100 story building and 6 Apatosaurus dinosaur eggs. 2- You have 81 story building and 3 ...
20
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 ...
8
votes
1answer
2k views

99 chips into more chips

You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot machine, someone comes to you and congratulates you that you have a chance to make more ...
12
votes
3answers
993 views

Day and night of the two timers

            Make a non - 24 - hour day /  night cycle       &...
9
votes
2answers
385 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 ...
8
votes
3answers
575 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 ...
7
votes
2answers
318 views

Square Spin #2: Climb the Mountain!

Square Spin History: #1>#2 New Rules This puzzle introduces two new square types: Unmovable squares (Un) Replaceable squares (Re) Plus the concept of ambiguity! Ambiguity of squares Certain ...
30
votes
5answers
6k views

Two spies throwing stones into a river

There is a puzzle about two spies: Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
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 ...
22
votes
7answers
3k 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 ...
9
votes
2answers
253 views

You Sign Me Right Round

This is a 9x9 grid, with a sign in the center cell like shown. You can add signs to this grid one at a time following these rules: Each sign placed must point to the next sign placed Placed signs ...
17
votes
5answers
1k views

Universal dissection

Alice has a squared paper 8 by 8. She cuts out one 1x1 square from it, at row N, column M. Bob cuts the rest of the paper into pieces. Once he is done, Alice asks Bob to put the pieces together in a ...
12
votes
2answers
7k views

Connect four towers by roads

Four guard towers are situated in a square formation of side length 1km. A general wants to build roads to connect the towers so that one can walk from any tower to any tower along the roads, possibly ...
12
votes
4answers
2k views

Get 6 pawns in file A or H

This is somehow inspired by my other chess related question: Possible pawn combinations How can you get 6 pawns (white or black) on a chessboard on the files A or H using legal moves? Start with a ...
10
votes
4answers
473 views

Largest and smallest hexadecagon with sides $1, 2, 3, \dots,16$

Of all hexadecagons lying in the cartesian plane, all of whose vertices are lattice points, and whose sides are of length $1,2,3,\dots,16$ in some order, which two have the largest and smallest area? ...
10
votes
2answers
586 views

Turn on all squares

Take a square grid of size $a\times b$, with all squares being off. You can tap a square, to reverse the state of that square and all squares located in the same column and row as the tapped square. ...
8
votes
2answers
504 views

Devouring Nobility

Provide, with the minimum number of moves, a legal chess game where all pieces are captured except the sixteen pawns and the two kings. Example of final configuration: Which is done in 21 moves: 1. ...
14
votes
2answers
1k views

How many clues are required to ensure Einstein's Puzzle is solvable?

I used to play Einstein's puzzles a lot when I was younger, and very quickly learned to assess quite rapidly whether I thought a puzzle would be a quick solve or more time-consuming, but I never ...
10
votes
2answers
1k views

Chess Bloodshed

This puzzle is the idea of Dmitry Kamenetsky in a comment of my puzzle Devouring Nobility. Find, with the minimum number of moves, a legal game where all pieces are captured except the two kings.
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 ...
7
votes
4answers
331 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 "...
7
votes
4answers
316 views

Savage Road Signs (Part 2)

Please read part 1 or this might be confusing Since part 1, you have replaced the stolen stickers and your daughter has forgiven you. The highway ended up being a full 700km long, so you are happy ...
1
vote
1answer
288 views

The counterfeit coin [duplicate]

You have 9 coins. One of the nine is counterfeit. The counterfeit coin can be distinguished by weight - it is heavier than the rest. Using a balance scale only twice, find the counterfeit coin.
27
votes
10answers
3k views

One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
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 ...
26
votes
6answers
5k views

A Special Parking Lot

There is a special kind of parking lot that stores special 1x1 cars that only can move to adjacent squares not including diagonals if they are empty (provided no car occupies the square). Every car ...
26
votes
4answers
3k views

1000 gold coins to share with the king

You are the knight of a great kingdom in an unknown world. Your king sent you to a dungeon and you killed the dragon and got 1000 gold coins from the dragon’s lair. Normally, you are supposed to give ...
24
votes
3answers
1k views

How much money can we make?

My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust PayPal, banks, or the postal service so transferring money over ...
16
votes
5answers
829 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 ...
32
votes
6answers
3k views

Swapping rooks in a 4x4 board

You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom. Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is ...
26
votes
2answers
2k views

The tilted labyrinth - Can you find the fastest path in this 3D-puzzle? (Simulator now included.)

This is a puzzle was inspired by the board game labyrinth, which I very much enjoyed as a kid. It either requires very good 3D-visualization skills in your brain or some paper & scissors work. (...
21
votes
2answers
661 views

Amoebas escaping the prison

There is an infinite grid of squares. In one of the squares, there lives an amoeba (marked as a circle in the following pictures). Amoebas cannot move, but they can perform their unique action: an ...
31
votes
5answers
3k views

Biggest army on a chessboard

Reminder: Everybody knows that we can place 8 queens in a chessboard without threatening each other (see here). Same reasoning can be applied for knights, bishops, rooks and kings. Giving ...
11
votes
1answer
578 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 ...
11
votes
6answers
808 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 ...
8
votes
3answers
479 views

Guess your hat color, but you don't have to

Here is the puzzle: N hats are put on N logicians, each hat color is selected randomly: black or white. As usual, every logician doesn't see the hat on his own head, but sees the rest. They cannot ...
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 ...