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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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15 votes
5 answers
1k views

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 ...
8 votes
1 answer
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, ...
8 votes
9 answers
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 ...
17 votes
2 answers
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 ...
12 votes
6 answers
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). ...
0 votes
1 answer
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
6 votes
4 answers
762 views

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 ...
-2 votes
1 answer
147 views

Make numbers 1 - 30 using the digits 2, 0, 2, 5

Try to make all numbers 1-30 using the digits 2, 0, 2, 5. Rules: Use all four digits exactly once. Allowed operations: $+,−,×,÷,! \text{ (factorial)}, !! \text{ (double factorial)}, !!! \text{ (...
1 vote
1 answer
141 views

Relation Between The Year And The Day

Today is January 22, the 22nd day of the year 2024. I chose today because 22 is my favorite number. Now for the problem. Try to relate 22 to 2024 using math. For example, 58 is related to 271 because ...
18 votes
11 answers
5k views

How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

I consider it an amazing though very challenging puzzle: 1 2 3 4 5 = 5 4 3 2 1 One must insert exactly five pluses (i.e. five addition signs) somewhere between those ten displayed figures in such way ...
5 votes
2 answers
438 views

SAD!!!...System Access Denied..you got three minutes to input three digit passcode

Hexagon is a super secret system with varying levels of access. Users do not have to remember any password. They just have to answer the questions posed by Hexagon strictly in the allotted time. Today ...
0 votes
1 answer
183 views

this puzzle is based

This message is a basic numeric substitution cipher. The key is the standard, regular alphabet in the correct order (ABC...XYZ). Here is the message: 3 16 15 7 20 1 22 23 13 1 22 10 16 15 21 27 16 23 ...
1 vote
0 answers
114 views

Can you find the missing letters?

A pattern of letters has had letters 10 through 20 deleted. Your job is to find out what letters should go in spots 10-20. Here is the pattern: a, b, c, d, d, d, f, e, f, _, _, _, _, _, _, _, _, _, _, ...
22 votes
2 answers
2k views

What is a RAP Number™?

Taking inspiration from "What is the word™" series, here the numbers conforms to a special rule, I call it a RAP number™. Use the following examples below to find the rule. RAP number™ NOT ...
12 votes
2 answers
824 views

What do 84, 96 and 108 have in common?

There's a certain property that's shared between (as far as I know) infinite positive integers including 84, 96 and 108. Below are the first thousand numbers with this property; I added that many in ...
12 votes
4 answers
679 views

Which positive integers have at least one positive integer multiple such that the base 10 representation of that multiple has only even digits?

Which positive integers N have the property that there exists at least one positive integer multiple of N such that the base 10 representation of that multiple has only even digits?
4 votes
1 answer
231 views

How many does 4 have?

I found out that 0 has none 1 has one 2 has two but 3 has none How many does 4 have?
-4 votes
2 answers
228 views

If ABCDE*4 = EDCBA. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?

If ABCDE*4 = EDCBA. ABCDE,EDCBA are five digit numbers. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?
5 votes
1 answer
536 views

This poem is titled Ζ-Gap

The answer is a two-digit number. Do whatever you want to play Solution is one step away Mine for alien harmony Take some notes you want to declare Regions you were so unaware Fundamental is always ...
13 votes
3 answers
1k views

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 ...
-1 votes
2 answers
435 views

Pick the odd one out: 214, 350, 520, 738

I am preparing for an exam(NTSE), and I came across this puzzle(aptitude) in one of the quizzes. book(study guide NTSE). The book's author is Arihant Experts. The question is to Pick the 'odd one out' ...
-2 votes
1 answer
272 views

Pick the odd one out: 146, 821, 704, 603 [closed]

I am preparing for an exam, and I came across this puzzle(aptitude) question. The question is to Pick the 'odd one out' and there are four options given. 146, 821, 704, 603 The correct answer is 603....
12 votes
1 answer
658 views

Dead By Daylight

This puzzle is a reference to a game, Dead By Daylight. Though you don't need a knowledge about the game. Consequently, there is no "video-games" tag. Story The Entity wants to have the ...
17 votes
1 answer
1k views

What is the Color Code™?

Inspired from Can you name the country code? and What is a Number™? series $ \begin{gather} % custom template - reuse if you may \def\S#1#2{\Space{#1}{21px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}}...
3 votes
1 answer
123 views

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. ...
3 votes
1 answer
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
1 answer
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 ...
2 votes
1 answer
172 views

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 ...
7 votes
2 answers
1k views

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 ...
15 votes
1 answer
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 ...
13 votes
1 answer
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
0 answers
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 ...
8 votes
7 answers
5k views

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?
13 votes
1 answer
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 ...
27 votes
1 answer
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 ...
11 votes
1 answer
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 ...
30 votes
1 answer
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 ...
4 votes
1 answer
255 views

Fractions and Fractional Numbers

Using fractions and fractional numbers of the digits $1$ to $10$ and only the mathematical operations of addition, subtraction, multiplication, and division, including parenthesis (e.g. $1 + 2 - (3 * ...
5 votes
1 answer
269 views

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 ...
3 votes
2 answers
323 views

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?
2 votes
1 answer
244 views

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, ...
2 votes
2 answers
414 views

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 ...
1 vote
1 answer
175 views

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 ...
0 votes
1 answer
333 views

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 ...
17 votes
2 answers
1k views

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 ...
7 votes
2 answers
1k views

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 ...
5 votes
1 answer
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 ...
14 votes
2 answers
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" ...
2 votes
1 answer
194 views

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. ...
16 votes
1 answer
1k views

What number goes in the ?? box?

A simple pattern puzzle What is the number in the ?? box? Why? No programming please.