All Questions
35
questions
2
votes
0
answers
48
views
Dividing $N$ coins into at most $K$ groups such that I can get any number of coins by selecting whole groups
Problem
Inspired from Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups . I am interested in the number of possible ways we can get such a split....
- 1,181
0
votes
1
answer
343
views
Why the "sum of permutation inversions" is a non-admissible heuristic for the 8-puzzle? [closed]
A heuristic h(N) is admissible if for every node N, 0 ≤ h(N) ≤ h∗(N) where h*(N) is the true cost to reach the goal state from N.
In my opinion, the true cost to reach the goal state from N is 21 for ...
1
vote
0
answers
287
views
Rephrase a simple mathy logic problem (yielding solution of an ordered procedure), and its generalized counterpart, into a solvable algorithm.
I'm given a selection of logic puzzles about different entities crossing a river safely (either from the same side to the same other side, or switching sides; utilizing the same boat, with certain ...
- 29
1
vote
2
answers
145
views
Couple problems and classic wolf/goat/cabbage and abstraction
I was reviewing Dijkstra's approach on the problem/puzzle of how 2 married couple can cross a river with 1 boat that can carry 2 people. The original problem's restriction is that the wife can't be in ...
- 1,609
2
votes
1
answer
157
views
Generallizing independent weighings solution for coin weighing puzzle
There is a puzzle that goes something like "you have $n$ coins with $m$ uses of s balance scale allowed; find out coin with the different weight" (normally given with $n=12$ and $m=3$).
...
- 161
4
votes
0
answers
159
views
Minimizing floor space needed to store $N$ unit cubes, subject to two placement rules
There is a store room which has only three sides all touching each other perpendicularly, the sides can be defined as: two infinitely large walls and one infinitely large floor.
There are $N$ cubes ...
- 61
8
votes
1
answer
769
views
Leapfrogs puzzle -- Least number of moves needed to interchange the pegs
This is a question from the book "Thinking Mathematically" by Burton and Mason.
Question: Ten pegs of two colors are laid out in a line of 11 holes as shown below.
I want to interchange the ...
1
vote
2
answers
195
views
Finding the maximum value of elements to be selected in a grid - ZIO $2009$, P$1$
Hello Community! The above problem you see is a problem I got wrong. :( This is ZIO $2009$, P$1$.
I tried the problem and miserably found the wrong answer as $20$. Here is how my approach goes - part ...
- 779
1
vote
3
answers
70
views
Minimizing the operations to be done on letters - ZIO $2014$, P$1$
Hello everybody! The above problem is a combinatorics problem I could not solve. :( This is ZIO $2014$, P$1$.
Here is my approach (feel free to point out any mistakes in it, that's why I am asking ...
- 779
1
vote
1
answer
157
views
Finding a binary sequence given sorted and end sequence - ZIO $2011$ P$4$
Hello everybody! The above problem you see is a combinatorics problem I could not solve. :( The answers are $00110111, 000111011011$ and $001111011101011$. This is problem $4$ from ZIO $2011$.
Notice ...
- 779
0
votes
0
answers
22
views
Minimizing the number of operations of subtracting one so as to get to $0$ [duplicate]
Hello Community! The above problem you see is a combinatorics problem, more like an algorithmic problem that I could not solve. :(
This problem requires that every child gets satisfied. In brief ...
- 779
2
votes
1
answer
412
views
Explanation of Freeman Dyson's solution of the counterfeit coin problem
Freeman Dyson's paper, The problem of the pennies Math. Gaz., 30 (1946) 231-234, offers a solution to a counterfeit coin detection problem. I quote his solution of one case as follows. I would ...
- 9,927
1
vote
1
answer
332
views
Generating all possible Domino tilings on a $4 \times 4$ grid
I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
- 11
5
votes
1
answer
163
views
Minimal number of questions to identify a subset
This is a curiosity question.
Recently I stumbled across the following problem :
Given three integers $k,m, n$ such that $m+k\leq n$. A friend chooses a subset $S\subseteq\lbrace1,\ldots,N\rbrace$...
- 13.8k
1
vote
0
answers
281
views
Cyclic Partisan Nim Variant
This game is played with a sequence of heaps and a position marker, where each heap is owned by exactly one player. The game ends when a player has removed all objects from their own heaps, and this ...
- 330
1
vote
1
answer
58
views
Pair Arrangement Problem
During Holiday meal we were thinking about a problem.
To simplify a real world case, let's say each couple of married parents have 2 children which are also married.
Each couple of parents want both ...
- 123
1
vote
2
answers
281
views
Brute force circle problem
Question:
The maximum number of individual regions formed by three lines dividing a circle is seven. The circle contains an ant colony and each region contains between one and seven ants. Can you ...
user517784
6
votes
2
answers
3k
views
Jugs of Water Puzzle: Minimum Number of Operations
PUZZLE. Given two water jugs with capacities $a, b \in \mathbb{N}$, the goal is to measure exactly $c$ units of water only performing the following operations:
fill one of the jugs to it's capacity ...
- 341
5
votes
2
answers
473
views
Coin weighing to find similar-weight sets
There are $n$ coins. You have a scale that, between two sets of coins, tells you which set is heavier, or if they are equal. What is the worst-case minimum number of weighings after which you can ...
- 7,194
1
vote
1
answer
728
views
A puzzle on coin weighing
We are given $(3^n-1)/2$ coins, and among those coins there is just one counterfeit coin. All the other coins weigh the same, but the counterfeit coin weighs slightly heavier or lighter (we don't know ...
- 1,107
29
votes
4
answers
4k
views
Each person has at most 3 enemies in a group. Show that we can separate them into two groups where a person will have at most one enemy in the group.
The question that I saw is as follows:
In the Parliament of Sikinia, each member has at most three enemies. Prove that the house can be separated into two houses, so that each member has at most ...
- 174
0
votes
2
answers
919
views
Repaint an 8x8 chessboard to reach only one black square. [closed]
The question I saw is as follow:
Assume an 8x8 chessboard. You can repaint all squares of a row or a colum or a 2x2 square. The goal is to attain one black square. Can you reach the goal?
- 174
4
votes
1
answer
380
views
What is the minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares? [closed]
What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares.
Notes:
-The squares to be drawn can be of any size.
-There ...
- 63
4
votes
3
answers
1k
views
Using up letters on a refrigerator is NP-complete
You spend some time with your preschool-age daughter trying to use up all of the magnet letters on the refrigerator to spell words that she knows. Formally, you have a set of letters and you are ...
- 61
0
votes
1
answer
883
views
The number of ways people standing in a line can be holding hands
I'm writing a program to analyze the maximum unique sequences of data in a string, given certain sets of two can be interpreted in two ways. There's a bit of math that I can't figure out, I've ...
- 1,851
9
votes
2
answers
6k
views
Numbering edges of a cube from 1 to 12 such that sum of edges on any face is equal
Assign one number from 1 to 12 to each edge of a cube (without repetition) such that the sum of the numbers assigned to the edges of any face of the cube is the same.
I tried a bunch of equations but ...
- 193
13
votes
3
answers
2k
views
Deducing correct answers from multiple choice exams
I am looking for an algorithmic way to solve the following problem.
Problem
Say we are given a multiple choice test with 100 questions, 4 answers per question (exactly one of those four being ...
- 346
1
vote
2
answers
4k
views
How do I find the maximum number of knights on a chess board?
I came across this problem and after thinking a lot I could not get any idea how to calculate it. Please suggest to me the right way to calculate it.
Given a position where a knight is placed on an ...
- 291
11
votes
1
answer
233
views
Given a desired coloring scheme for a stick, how can I brush it with the fewest steps?
If I want to color a stick (regarded as a line segment in one-dimensional space) to a desired coloring scheme using brush, how can I make it with the fewest steps?
Notice that, new color will just ...
- 263
0
votes
1
answer
458
views
Combinatorics puzzle
I am having a problem dealing with following topic:
lets say we have set of numbers n = [ 1 2 2 3 ] and we want be able to get all two-elementary combinations out ...
- 103