# Questions tagged [number]

A competition to solve a particular problem through the usage and manipulation of numbers.

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### Fastest square root of an arbitrary size

We do seem to have a fastest square root challenge, but it's very restrictive. In this challenge, your program (or function) will be given an arbitrarily sized nonnegative integer, which is the square ...
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### Make a minimal and maximal 2-digit number from digits of two 3-digit numbers

Let's solve this user's homework; I think it's an interesting exercise! Input Two 3-digit natural numbers. Outputs Two 2-digit numbers. In each of the output numbers, one digit is taken from one input ...
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### Prefix divisibility

Inspiration Given a positive integer $1 \le n \le 9$, output all positive $n$-digit integers $i$ for which the following is true: Each digit from $1$ to $n$ appears exactly once in $i$. ...
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### Square root of a base 10 positive integer, digit by digit [closed]

It is possible (Wikipedia reference) to compute the square root of any number in a digit by digit fashion using a simple (I had learned it in primary school) algorithm. Challenge: read a positive ...
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### Golf a bijection $\mathbb{N}^n\to\mathbb{N}$

Your task is to write a program which implements a bijection $\mathbb{N}^n\to\mathbb{N}$ for $n \ge 1$. Your program should take $n$ natural numbers as input, in any acceptable method (including ...
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### Count the Collatz survivors mod 2^n

Introduction We have 22 Collatz conjecture-related challenges as of October 2020, but none of which cares about the restrictions on counter-examples, if any exists, to the conjecture. Considering a ...
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### We're much closer than you think

Martin Ender's 2D programming language Alice has two different modes depending on what orientation the IP has: orthogonal (Cardinal mode) or diagonal (Ordinal mode). Commands in Alice change their ...
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### Eating Persistence

Intro Find the result of number cannibalism. Why was 6 scared of 7? Becase 7 8 9. Your program will have to find the result of applying the ...
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### Size up a number

Intro Given a whole number $< 100,$ extend/shorten the english representation of the number to have as many characters as it's value. Sandbox Rules Take the number $n$, and get it in words ...
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### Amount Of Potential Keys That'll Fit The Lock

Introduction: You're a key maker, and want to access something from a safe that has a lock. Unfortunately, the key to that lock is lost, so you'll have to make a new one. You have access to a bunch of ...
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### Find a Similar Number

We consider two integers to be similar if, when written in decimal, have the same length, and if we compare characters in any two positions for both decimal strings, the comparison results (less, ...
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### Convert to and from Base 94

The challenge Make 2 programs which convert decimal to and from base 94, or a bidirectional program. Base 94? Base 94 is like any other base, but instead of 0 to 9 and letters, it uses ASCII ...
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### A bit of a digital XOR

Here are the first 100 numbers of a sequence: ...
We know that not all fractions have a terminating binary representation. However every fraction can be written as a leading portion followed by a repeating portion. For example $1/3$ starts with $... 9answers 808 views ### Mad Libs number sequences My robot for generating Mad Libs-style sequence challenges has gone rogue! To defeat it, I need you to write code that can solve all the challenges it can crank out. Your input is three selections ... 11answers 3k views ### Any lips images Introduction The$n$-ellipse is a generalization of the ellipse with possibly more than two foci. Specifically, given$n$points on the plane, called foci, the$n$-ellipse is the set of points ... 8answers 1k views ### Counting Distinct Real Roots of Low-Degree Polynomials Challenge: I want to know about the real roots of polynomials. As a pure mathematician, I care about the existence of such roots, rather than their numeric values. The challenge is to write the ... 22answers 4k views ### Find self-locating strings in a number Based on this Numberphile video A self-locating string is a number (or set of numbers) in a decimal expansion which corresponds to its location, from the start of the decimal. For example, take the ... 5answers 869 views ### How many unique one sided polyominos Context From Wikipedia: A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. one-sided polyominoes are distinct when none is a translation or rotation of ... 37answers 2k views ### Is it a doubling sequence? A doubling sequence is an array of numbers where each subsequent number is at least twice the previous number. Given an ordered list of numbers, determine if the numbers in the list ($n_{x}$) have ... 5answers 201 views ### Count switches in a smallest square root sequence mod$2^n$Definition For any$a\equiv1\ (\text{mod }8)$and$n\ge3$, there are exactly 4 roots to the equation$x^2\equiv a\ (\text{mod }2^n)$. Now, let$x_k(a)$be the smallest root to the equation$...
Definition We say a pair of integers $(a,b)$, where $0<a<b<N$ and $N$ is an integer larger than 4, is an inverse neighbor pair respect to $N$ if $ab\equiv1\text{ }(\text{mod }N)$ ...