# Questions tagged [number-property]

Puzzles that use number properties such as even and odd, multiples of numbers, part of a well-known sequence (i.e. Fibonacci) or theorem (Pythagorean relations) or others in part of the method to solve the question.

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### Geometry Puzzle: Tangent Circles with Integer Radii

Take as a semi-related example a series of circles with radii 10, 9, 8, ..., 2, 1. Place the first (largest) circle in the center and subsequent circles around it, keeping tangency between subsequent ...
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### Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard. Bob appends another digit from the set M until a 2n-digit ...
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### Getting The Numbers 33 Through 99 Only Using 2, 0, 2, and 4 [closed]

How do you get the numbers 33-99 by using the numbers 2,0,2,4
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### How to get the numbers from 50 - 100 with the numbers 2, 0, 2, 4

All I need is 56-59, 69, 73, 75- 77, 79, 86, 90-94, 99. I've done the rest but I would love to hear other solutions. Rules: Use any of the following operations: basic operations (+ - x /), to the ...
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### Consecutive integers which have digital sums that are not relatively prime

What are ten smallest natural numbers n, such that n and n+1 have digital sums which are not relatively prime?
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### What number comes next in this evenly doubled sequence?

I've been playing around with sequences lately and found a pretty evenly doubled sequence of single digit numbers: 1, 12, 30, 64, 65, 156, 175, 368, 369, 371, 752, 753, 1524, 1525, 3060, 3073, 6168, ...
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### An oddly formed sequence?

I've been playing around with sequences lately and came across one that was rather, odd. $101$, $123$, $147$, $189$, $191$, $213$, $217$, $279$, $...$ Hints Let $N_i = 101$... Can you determine the ...
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### A dance between numbers

Given the following equation: $$\Delta = \Biggl(\frac{t \mod 6}{(t \mod r) + 1}\Biggr)^2$$ Find the relationship between $t$ and $r$, along with the properties of each, that ensures $\Delta = 9$. For ...
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### The maze of everlasting flowers

You were recently caught trespassing on the queen's hunting grounds. The punishment for this crime is a miserable experience the locals call the maze of everlasting flowers: The full resolution of ...
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### Scrabble with prime numbers!

How to Play Overall, gameplay is very similar to typical Scrabble; however, unlike typical Scrabble, you'll be using digits instead of letters (we'll cover your tile bag later). The objective is to ...
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### The digits of the cube of a 3-digit number X

The digits of the cube of a certain 3-digit number X are, from left to right, the square of a 2-digit number, followed by the square of another 2-digit number, followed by one digit. (Everything is ...
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### Integers containing all ten digits

It is known that most positive integers contain at least one copy of each of the ten digits. What is the largest n such that at most 50% of the integers in the set [1,2,3,...,n] contain at least one ...
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### Mapping days as a 4 digit number! [closed]

I have a puzzle that includes mapping days as a 4 digit number. Sunday: 6137 Monday: 6240 Tuesday: 7358 Wednesday: 9497 Thursday: 85?? The first digit is just the number of characters and the second ...
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### The largest Saturday number

No weekend love yet shown, therefore I will fix that. A Saturday number is a number in which for all $1 \le i \le l$, where $l$ is the length of the number, the first $l$ digits (from the left) divide ...
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### Largest number with no repeating digit pairs

What is the largest whole number that you can form, such that no pair of consecutive digits occurs more than once? For example you can have 34543, but you cannot have 34534 as the pair "34" ...
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### Adding up divisors of integers

Alice and Bob play a game, taking turns. Alice starts and writes an integer between 1 to 10 on a blackboard. Then Bob adds any integer between 1 to 10 to this number and writes it on the blackboard. ...
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### Making a 10 digit number divisible by 3

Alice and Bob play the following game, taking turns. Alice starts and writes a single digit from 0 to 9 at the blackboard. At every turn, each player adds a single digit at the right of the current ...
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### What number goes in the ?? box?

A simple pattern puzzle What is the number in the ?? box? Why? No programming please.
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### Odd numbers to Even numbers

Remember the old puzzle? "Can you take just one letter out of an odd number and make it even?" Note the clever wording. It just says make it even; not "make it an even number"... ...
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### Largest 5-digit palindrome in base 16, where each digit appears at most twice

What is the largest number $x$ such that $x_{16},$ i.e. $x$ in base 16, is a 5-digit long palindrome, where each digit appears at most twice? A palindrome is a number that reads the same forward ...
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### When should this question be answered?

If you hover your mouse over the time marked in the right-bottom corner of this post, then you will see a string showing the exact time that I post this question, which reads ...
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### What is the house number in nolteight street

Alice moved to nolteight street. Bob meets her after her move, and he knows that the smallest house number in nolteight street is 8, and the highest number is 100. But he does not know Alice's house ...
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### Consecutive integers with digit sum divisible by 19

What is the smallest positive integer N, such that the digit sum of N and N+1 are both divisible by 19?
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### A function. Really?

If you give me a 5, I give you a 21. If you give me a 6, I give you a 2. If you give me a 7, I give you a 12. If you give me a 10, I give you a 101. What am I processing to get the result? Hint 1 ...
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### When do decimal-coded binary numbers XOR to zero?

Background definition: XOR on numbers Given two non-negative integers $x$ and $y$, let $x\oplus y$ denote the bitwise exclusive or (XOR) of the numbers $x$ and $y$. This is the result of writing $x$ ...
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### Sort 10 clock numbers

An electronic clock shows hours and minutes: from 00:00 to 23:59. Sort the numbers 0, 1, ..., 9 according to the time of their presence on the clock board during the 24-hours. Edit For example, for ...
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