# 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 ...
410 views

### What is a Good Pasta Number™?

This puzzle is inspired by JLee's What is a Word/Phrase™ series and the subsequent "Number" variants. (Actually, I'd originally tried to create a more original puzzle using the same idea, ...
2k views

### Multilanguage generalization of "What number is that? Asks Grandpa"

This is a multilingual generalized follow-on to "What number is that? Asks Grandpa", which I restate as: "What is the smallest positive English integer N, for which if you take its WORD anagram and ...
2k views

### 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 ...
10k views

### Make numbers 1 - 30 using the digits 2, 0, 2, 4

Try to make all numbers 1-30 using the digits 2, 0, 2, 4. Rules: Use all four digits exactly once. Allowed operations: $+, -, \times, ÷, !$ (factorial), x^y (exponentiation), √ (square root). ...
166 views

### 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 ...
147 views

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### Digital Digits Magic Square 3x3 that can be rotated 180 degrees

In the below image we have a magic square of a size 3x3. The magic number for all its rows, columns and both diagonals is 165. Rotate the grid 180 degrees and all sums still have the magic number 165. ...
202 views

### A Weird Sequence

Today, I was in Rome for a vacation. The most peculiar thing happened. A gnome walked up to me. Uttering no words, it handed me a slip of paper. 0, 1, 1, 2, 3, 2, 5, 5, 5, 9, 4, ? Naturally, I was ...
1 vote
410 views

### How many combinations can you make with 3 digits?

So my mom- a teacher - called me and my brother and gave us each a paper and pencil. She said: Think of three distinct single digit positive integers (0 to 9) and write down as many numbers (number ...
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### Consider the equation a?b?c =d [closed]

Consider the equation a?b?c =d. Here a, b and c are 3 distinct integers from 0 to 9 (both inclusive) and "?” represents any signs out of “+", "-", “x” of “÷”. Note that the 2 ...
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### What is a Finale Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a Finale Number™. Use the following examples ...
358 views

### What is a Hope & Love Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a Hope & Love Number™. Use the following ...
389 views

### What is a Voluminous Number™?

In the spirit of the What is a Word™/Phrase™ series started by JLee, a special brand of Phrase™ and Word™ puzzles. If a number conforms to a special rule, I call it a Voluminous Number™. Use the ...
1 vote
186 views

### I wonder what that would be

This is my own puzzle. Consider the following Alice begins march for peace in East Bengal along with Gandhi Bentley celebrated the first Bahia Independence Day Catherine saw the starting of the Great ...
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### How can four be the half of five? [closed]

I came across this enigmatic one-liner: How can four be half of five? Can you figure it out?
876 views

### 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 ...
2k views

### What is a Chess Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a Chess Number™. Use the following examples ...
847 views

### What is an IJKLMN Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it an IJKLMN Number™. Use the following examples ...
2k views

### What is a BEN Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a BEN Number™. Use the following examples ...
255 views

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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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### 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 ...
216 views

### 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 ...
2k views

### 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" ...