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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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A robin-round tournament, where 20 % of all games were draws and half of teams did not win. How many teams were there? [closed]

Several teams have participated in a soccer tournament. It was a round-robin tournament where each team played each other exactly once. Every single game ended up either in a draw or in a victory for ...
Alexander's user avatar
  • 595
12 votes
5 answers
842 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 ...
Brandan's user avatar
  • 143
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 ...
ThomasL's user avatar
  • 12.2k
0 votes
1 answer
161 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
user88484's user avatar
6 votes
4 answers
756 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 ...
bob's user avatar
  • 79
-2 votes
1 answer
141 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{ (...
WOWOW's user avatar
  • 439
1 vote
1 answer
139 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 ...
Ronchen Luo's user avatar
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). ...
jac's user avatar
  • 137
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 ...
Alexander's user avatar
  • 595
0 votes
1 answer
181 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 ...
ᵍʰᗣˢᵗ's user avatar
1 vote
0 answers
112 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, _, _, _, _, _, _, _, _, _, _, ...
BigMistake's user avatar
12 votes
2 answers
812 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 ...
Peter's user avatar
  • 613
4 votes
1 answer
230 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?
RogerA's user avatar
  • 6,627
-4 votes
2 answers
221 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?
jkj's user avatar
  • 21
12 votes
4 answers
678 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?
Will.Octagon.Gibson's user avatar
5 votes
1 answer
535 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 ...
Dannyu NDos's user avatar
  • 5,247
-1 votes
2 answers
426 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' ...
Max's user avatar
  • 123
-2 votes
1 answer
261 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....
Max's user avatar
  • 123
3 votes
1 answer
122 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. ...
Maff's user avatar
  • 621
3 votes
1 answer
201 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 ...
shreyasm-dev's user avatar
1 vote
1 answer
394 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 ...
RogerA's user avatar
  • 6,627
2 votes
1 answer
170 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 ...
Epic's user avatar
  • 47
6 votes
0 answers
266 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, ...
Auride's user avatar
  • 797
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 ...
Suzuna Minami's user avatar
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?
Hexagonal Impossibilities's user avatar
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 ...
PiGuy314's user avatar
  • 2,436
4 votes
1 answer
251 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 * ...
DrD's user avatar
  • 39.3k
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?
Bernardo Recamán Santos's user avatar
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, ...
Hazel へいぜる's user avatar
1 vote
1 answer
174 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 ...
Hazel へいぜる's user avatar
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 ...
Hazel へいぜる's user avatar
0 votes
1 answer
330 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 ...
Hazel へいぜる's user avatar
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 ...
Hazel へいぜる's user avatar
5 votes
1 answer
210 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 ...
user avatar
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 ...
Bernardo Recamán Santos's user avatar
5 votes
1 answer
268 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 ...
codeingerman's user avatar
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 ...
SegFaultPlus4's user avatar
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" ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
193 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. ...
ThomasL's user avatar
  • 12.2k
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 ...
ThomasL's user avatar
  • 12.2k
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.
DrD's user avatar
  • 39.3k
5 votes
2 answers
236 views

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"... ...
DrD's user avatar
  • 39.3k
0 votes
1 answer
131 views

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 ...
Outsider's user avatar
  • 111
8 votes
3 answers
2k views

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 ...
WhatsUp's user avatar
  • 7,407
3 votes
2 answers
175 views

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 ...
ThomasL's user avatar
  • 12.2k
9 votes
1 answer
492 views

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?
ThomasL's user avatar
  • 12.2k
3 votes
1 answer
150 views

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 ...
math scat's user avatar
  • 1,137
7 votes
2 answers
577 views

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 $x$ ...
A. Rex's user avatar
  • 955
5 votes
2 answers
583 views

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 ...
Nick's user avatar
  • 1,695
3 votes
1 answer
199 views

What is so unique about these four numbers?

These four numbers look like four ordinary numbers. But I found something unique about these four that I may be only true for one other set of numbers-- unless you raise the bar-may be. So what is ...
DrD's user avatar
  • 39.3k