All Questions
17
questions
3
votes
3
answers
349
views
How to think and deduce optimal strategy move for both Alice and Bob
Question:
Alice and Bob are playing a game on a one-dimensional number line. Initially, Alice is standing at coordinate $x=a$ (integer) and Bob is standing at $x=b$ (integer) .It is guaranteed that $...
- 55
1
vote
1
answer
140
views
Difficulty with a Combinatorial Math problem
I was doing this question from a national mathematical olympiad and although I couldn't solve it but I found something but don't know how to progress.
For a positive integer $N$, let $T(N)$ denote the ...
- 131
0
votes
0
answers
233
views
Can we arrange $\{1,...,9\}$ in $3\times 3$ grid so the set of products of rows equals the set of products of columns? [duplicate]
I find a interesting question of Prmo mock and Promys 2020
For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the ...
user1147681
0
votes
1
answer
71
views
find all good numbers between 500 and 528
For which positive integers $500\le n\le 528$ does there exist a positive integer k so that the numbers from 1 to 3k can be split into k pairwise disjoint subsets, each of size 3 and each of which ...
- 2,031
2
votes
2
answers
372
views
The number of four-digit numbers that have distinct digits and are divisible by $99$
We try to find the number of four-digit numbers that have distinct digits and are divisible by $99$.
Let a number be $N = abcd$, then we have $9| N$ and $11|N$.
Thus $9| a+b+c+d$ and $a+c \equiv b+d \...
- 12.7k
5
votes
1
answer
238
views
Interesting cyclic infinite nested square roots of 2 and cosine values
It is interesting to note that any angle between 45° to 90° satisfying $1\over4$ < $p \over q$ <$1\over2$ where $ p \over q$ is of form $p = 2^n $ and $q$ is an odd number satisfying $2^{n+1} &...
- 1,017
3
votes
1
answer
1k
views
Distance formula for generalized knight movement on infinite chessboard from a corner
Consider a chessboard infinite in positive x and y directions, all square has non-negative integer coordinates, and the only corner is at $(0,0)$. A $(p,q)$-knight is a piece that can move so that ...
- 814
1
vote
1
answer
120
views
Existence of 2006 distinct natural numbers
Does there exists $2006$ distinct natural numbers such that the sum of any two divides the sum of all the given numbers?
- 165
1
vote
0
answers
87
views
Numbers made from digits 1-9 -- proving the exceptions?
Inspired by this paper
Introduction
In this paper, a sequential representation of a number is a formula that uses the digits 1-9 in order with the mathematical operations +, -, ×, ÷, ^, as well as ...
- 4,472
4
votes
1
answer
73
views
On the GCD of two palindromes.
I had an observation. Which I will discuss below. My question will be Is my observation correct? If so, how can one prove it?
Observation:
Consider the string of palindromes below:
$100...01$ and $...
- 2,190
2
votes
1
answer
521
views
Optimization and Postage Stamp Problem
(1)
Given the set U = {1, 2, 3, ..., 98, 99, 100} of Natural numbers, find the smallest subset S contained in U that:
For every element v belonging to U, there are a, b elements of S, not ...
- 21
13
votes
1
answer
403
views
Combinatorial prime problem
Update
As Barry Cipra noted in the comments, a better framing of the question might be that I'm looking at absolute differences $|a−b|$ or totals $a+b$ for $5$-smooth numbers $a$ and $b$ satisfying ...
- 9,018
0
votes
1
answer
126
views
Combinatorial prime puzzle
Is it true that no prime larger than $241$ can be made by either acting or subtracting $2$ coprime numbers made up out of the prime factors $2,3,$ and $5?$
Update
Above example is clearly wrong, as ...
- 9,018
2
votes
0
answers
158
views
Describing the sequence A224239.
I've been trying to describe mathematically the $n$th term $a_n$ of the sequence A224239. We get $a_n$ by counting the distinct ways to fill an $n\times n$ grid with squares of smaller integer size, ...
- 45.7k
5
votes
1
answer
117
views
Hockey Classics at Matheletics '13
I'm trying to solve a challenge from Matheletics '13:
Micheal Nobbs is organizing a training camp for identifying new talents in Indian Hockey. The camp witnessed a total of ($3K+1$) players. Each of ...
- 443