1
vote
1answer
49 views

How many bit strings of length 15 have exactly three 0s?

I need help with this question: How many bit strings of length 15 have exactly three 0s?
0
votes
2answers
75 views

how to find taxicab numbers but for squares?

Natural numbers that can be written as the sum of squares in two or more ways. The first ten numbers are 50, 65, 85, 125, 130, 145, 170, 185, 200, 205. $$ n = a^2 + b^2 = c^2 + d^2\\ a^2 − c^2 = d^2 ...
0
votes
0answers
30 views

How to calculate the number of combinations of getting a pair in a deck of 52 cards?

I am confused over calculating the number of ways in which I can select a pair out of a deck of 52 cards, this is how I go about solving the problem, following the definition of a pair in card games, ...
0
votes
2answers
107 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
4
votes
1answer
88 views

General approach to puzzles such as the “6 books puzzle”

Six different books (A,B,C,D,E,F) of identical size are stacked as in the figure. We know A and D are not touching. E is between two books which are both vertical or both horizontal. C touches ...
-1
votes
2answers
120 views

Proving $1 + 1 = 2$ [duplicate]

How do you break down the theory of $1 + 1 = 2$? How do you provide a proof, please be precise. This is for one of my discrete math courses and I don't know how this is relevant to the course. And ...
0
votes
1answer
65 views

Proving using squeeze principle

This problem sounds very confusing. Please help me solve this problem.
1
vote
0answers
22 views

Convex quadrilateral

In a convex quadrilateral (the two diagonals are interior to the quadrilateral) prove that the sum lengths of the diagonals is less than the perimeter but great than one-half the perimeter.
0
votes
3answers
87 views

How to find the planar embedding of a graph in general?

I need to find the planar embedding of a graph in general if one exists and specifically want to solve the problem for the graph in the figure below. I am acquainted with the graph algorithms but have ...
4
votes
1answer
77 views

Expected number of clusters on chessboard

N distinct squares are selected uniformly at random on an MxM chessboard, what is the expected number of clusters? A cluster is a collection of squares which are connected sideways, not cornerwise.
1
vote
1answer
215 views

The 100 Coins Puzzle

There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of ...
0
votes
1answer
23 views

Range of Numbers

I have a list of 25 spots and I know Value #1 and Value #25. What is the best way to estimate the values in between: Example: 1: 250,000 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ...
-1
votes
6answers
107 views

How do I construct a sequence of N numbers such that they are decreasing and they sum to 1? [closed]

How do I construct a sequence of N numbers such that they are decreasing and they sum to 1? In my case N is 22. That is, I need to create 22 values that decrease, and they sum to 1.
0
votes
1answer
271 views

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area?

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area geometrically ?
3
votes
3answers
145 views

Trying to work out the probabilities of a dice game I used to play

At college, my friends and I would sometimes waste time playing a game with dice. We would roll 25 dice, pick out all the dice that landed on a 6, then roll the rest. This would carry on until all the ...
1
vote
1answer
299 views

How many $n$-disk legal configurations are there for the Tower of Hanoi?

This question comes from this homework assignment from ECS20 at UC Davis. How many $n$-disk legal configurations are there for the Tower of Hanoi? A "legal configuration" means that no disk is ...
-4
votes
3answers
202 views

In how many ways can $16 be divided among 4 people? [closed]

In how many ways can $16 be divided among 4 people, assuming that each person has to get something and there are 5 cent coins and up
2
votes
1answer
65 views

How to derive a generating function for the following series

Given an integer n how would derive a function fn that is without conditional statements, does not use ...
33
votes
5answers
993 views

How much weight is on each person in a human pyramid?

After participating in a human pyramid and learning that it's very uncomfortable to have a lot of weight on your back, I figured I'd try to write out a recurrence relation for the total amount of ...
0
votes
1answer
138 views

Discrete mathematics for someone from a non-mathematical background

I have been a software programmer for over six years and I'm from a non-mathematical background. Though I had some limited exposure to discrete mathematics in my college years it didn't leave any ...
16
votes
1answer
561 views

How many different shapes can I make with this toy?

I have the following toy, perhaps some of you have seen it before. It consists of a bunch of cubes with an elastic string in the middle. You can bend it into different shapes like this: Or this: ...
4
votes
1answer
169 views

Board $7\times 7$ problem

An aid in this problem: On a board of $7 \times 7$ each box is painted red or blue so that any square on the board has at least two neighboring boxes blue. determine as little blue boxes that can be ...
-1
votes
1answer
56 views

Is it possible to merge two teams of final rankings with one team having 7 members, and the second team having 24 members?

Is it possible to merge two teams of final rankings with one team having 7 members, and the second team having 24 members? Is there a formula to provide one total overall ranking between the groups? ...
12
votes
2answers
672 views

9 pirates have to divide 1000 coins…

A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. Arriving on a deserted island, they now have to split up the ...
1
vote
2answers
89 views

How can be done by the method of mathematical induction?

We are given that $P(x+1)-P(x)=2x+1$ We also know that $P(0)=1$ We want to prove that $P(2004)=(2004)^2 +1$ Can someone explain how can be solved with mathematical induction? Thank you in advance!
3
votes
2answers
225 views

How to form pairs in a group so that each element is coupled with each other only once

My question is derived from real life but I think it's a classic mathematical problem. My uncle wants to organize a group activity with 12 people and wants to start by pairing each person with each ...
2
votes
1answer
46 views

Total length of pieces after splitting

If I consider the number line from $0$ to $n$ and cut it into $x$ pieces, it is well known that there is at least one stretch of length at least $n/x$. My question is what is the minimum total length ...
27
votes
2answers
411 views

Can a collection of points be recovered from its multiset of distances?

Consider $n$ distinct points $x_1,\dots,x_n$ on $\mathbb{R}$. Associated to these points is the multiset of all distances $d(x_i,x_j)$ between two points. Suppose one is only handed this multiset (you ...
1
vote
0answers
39 views

maximising the frequency of mode.

I have 4 numbers 5,5,3,1. Now I have the number 5, which I can distribute in any manner to ...
1
vote
1answer
104 views

Discrete Maths question

Show that $S=\{1,3,4,5,9\}$ is a difference set for $\Bbb Z_{11}$. Identify the design produced from $S$ by the sets of the form $S+i$, $i \in\Bbb Z_{11}$.
1
vote
1answer
47 views

How to get range of 1 to 10 by index?

I have a collection of lessons divided by levels Each level has 10 chapters. ...
0
votes
1answer
754 views

Can this crate have even numbers in all rows and columns?

A milk crate holds 24 bottles in four rows and six columns. Can you put 18 bottles of milk in the crate so that each row and each column of the crate have an even number of bottles in it?
5
votes
2answers
241 views

Sum(Partition(Binary String)) = $2^k$

So given any binary string B: $$b_1 b_2 \dots b_n$$ $$b_i \in \{0,1\}$$ It would seem it is always possible to make a partitioning of B: $$ b_1 b_2 \dots b_{p_1}|b_{p_1 + 1}b_{p_1 + 2}\dots ...
18
votes
2answers
815 views

What is the millionth decimal digit of the (10^10^10^10)th prime?

What is the millionth decimal digit of the $10^{10^{10^{10}}}$th prime? (This prime is, of course, far larger than the largest currently "known" prime, the latter having nearly 13 million ...
5
votes
5answers
6k views

How many bananas can a camel deliver without eating them all?

This is a fun puzzle I was assigned on the first day of highschool (over a decade ago). I just dug it up randomly from under my bed and thought I'd share it with the SE community. At the time, I ...
0
votes
1answer
563 views

Units of Hamming, and Euclidean distance

This is just a simple doubt I wanted to clear. I'm calculating the Hamming and Euclidean distance between two columns in a matrix, where each column is storing time information in seconds of when a ...
11
votes
3answers
3k views

Lights out game on hexagonal grid

I greatly enjoyed the Lights Out game described here (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page). Its mathematical analysis is here (it's just ...
6
votes
2answers
330 views

Watchdog Problem

I just came up with this problem yesterday. Problem: Assume there is an important segment of straight line AB that needs to be watched at all time. A watchdog can ...