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Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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8
votes
6answers
3k views

Move a single match to make this expression true

Move a single match to make the following expression true: So far I've found 6 valid solutions, can you find all 6? (or more!) Edit: Lots of great, creative answers! All 6 I found are represented ...
8
votes
5answers
1k views

The Great Houdini's awesome card guessing trick (2)

The Great Houdini is performing again! Everybody wants to see the famous magician and the magic show is sold out. Today Houdini shows the following sophisticated trick: A guy from the audience ...
7
votes
1answer
565 views

This ant sure is smart. But how fast is it?

A mad scientist uses ethically questionable methods to study the spatial cognition of ants. Last time, he left his lab ant in a cubic room and filled it with painfully intoxicating gas, capable of ...
7
votes
2answers
747 views

Write a true self-reflective statement about the digits from 0 to 9 (or prove it can't be done)

This statement contains 3 0's, 1 1, 4 2's, 1 3, 5 4's 92 5's, 6 6's, 53 7's, 58 8's, and 9 9's. Clearly that statement is incorrect. It only has 1 occurrence of ...
7
votes
3answers
1k views

3x3 “Magic Square” of Prime Numbers — Part II

Glad to know the previous puzzle, which was the first puzzle I posted in Puzzling, was warmly welcomed (Thank you!), and an optimal solution was found. Inspired by the comments there, here is the ...
7
votes
1answer
1k views

What is the missing number in the figure?

I have no idea what is, no logic ... but probably I am missing something
7
votes
4answers
2k views

Smallest number containing the first 11 primes as sub-strings

113257 contains the first 6 primes as sub-strings when reading them from left to right: 2: 113257 3: 113257 5: 113257 7: 113257 11: 113257 13: 113257 What is the smallest number that contains ...
7
votes
2answers
416 views

Find $n^{23}$ with the least multiplication

$n$ is an arbitrary real number. By only using multiplication, you are asked to find $n^{23}$ with the least amount of multiplication operation. Note: You can only use $n$ or the results you can with ...
7
votes
3answers
581 views

The Ebbozonian coin weighing puzzle

In the country of Ebbozonia, there are only two type of coins: light coins and heavy coins. The weights of these coins satisfy the following properties: All light coins have the same weight $L$. All ...
6
votes
1answer
577 views

Don't clear your terminal history 3

Previously, on terminal use... The door opens and you find yourself in a cave. After a short walk, you enter a small rectangular area, with a couple of fires towards the far side illuminating the ...
6
votes
2answers
5k views

Martin Gardner - Persistence

A number's persistence is : The number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number Then multiplying all the digits of that number ...
6
votes
2answers
534 views

Odd birthdate surprise

Last year, just before my birthday in February, I noticed something unsual. The last two digits of my birth year were the same as my age. How old was I then and was this an unusual occurrence?
6
votes
2answers
154 views

Swapping knights

On a $3\times3$ grid we have: with $8$ moves needed to swap the red and blue knights. What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
6
votes
2answers
511 views

I'm trying to create a magic square

I'm having trouble trying to make a $3\times3$ magic square with magic number $12$ and I can't figure it out. Can you please help me?
5
votes
2answers
174 views

Standard Sudoku Specialized with just 2 Primes

A standard 9x9 Sudoku uses the digits 1 to 9. You are only allowed two distinct primes to represent 1 to 9. Find out the minimum number of characters (digits + signs) needed to construct a Sudoku ...
5
votes
3answers
228 views

Find this Unique UVC Palindrome ( ignoring signs and decimal) from Given Fractional Relationship

Given: U, V, C are three distinct digits ( 0 to 9 ). UVVVV and CVVVV.U are concatenated numbers. Dot “.” Stands for decimal. Relation: $UVVVV/C= CVVVV.U$ Find U, V , C
5
votes
2answers
1k views

How many digits can be removed from a division puzzle?

Similarly to How many digits can be removed from a multiplication puzzle and still give only one answer? I am curious about division puzzles. I know this puzzle: . It has only 2 out of 42 digits $\...
5
votes
2answers
470 views

Make 439204 from Φ (Golden Ratio)

In my last formation-of-numbers question I somehow tricked myself, because I wanted to make a puzzle about a number that looks like a year. But the complicated solution I thought of turned out to be ...
5
votes
7answers
1k views

9sums - a logical deduction puzzle

Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers. --- --- --- --- 13 14 11 --- --- --- --- 11 ...
5
votes
3answers
961 views

Crack the Code #3

You return to the bench after cracking the last code, and you notice an envelope on the ground directly under it. You put down your envelope with the previous code and pick up the new one, ...
5
votes
4answers
775 views

An addition problem

Considering that 50+20=60 and 60+30=72, what's 40+30? Edit (now that this has been answered, I can state): This was earlier posted to alt.usage.english as ...
5
votes
1answer
304 views

Saving The Mayor (Part 2)

– Saving the Mayor, Part 2 – To play Part 1, click this link- Find the Cell Number, free the Mayor PART 2 – Saving the Mayor (Again....) It’s another cold day off the East of France. It was as if a ...
5
votes
1answer
204 views

Word Matrices, Level 2

This puzzle is based on NeedAName's recent puzzle, Determinant of Word Matrix. The challenge: Create a $3\times3$ matrix of distinct letters (i.e. no repeated letters) with no vowels in the ...
5
votes
1answer
131 views

21sums - more constraints

My initial question had lots of answers, as we can practically choose the middle square to be anything we want, and work outwards to the exterior edges, with the corners providing the flexibility ...
5
votes
2answers
213 views

Arranging a long line of cards

Annie has a very long line of cards, numbered from 1 to $n$, such that every odd card is face-up and every even card is face-down. The only way she can modify the line is by taking any segment of ...
5
votes
8answers
4k views

How to use 2,0,1,8 to make 51? [closed]

How to use the number 2,0,1,8 to make 51? You can use any operation except for multiple factorials and you can concatenate numbers, ex.2,0=>20 You can take the square root of a number without a ...
5
votes
4answers
876 views

Why did this prime-sequence puzzle not work?

While attacking a recent puzzle (whose solution ended up being entirely different from what I was trying), I was inspired to create a number-sequence puzzle with a sequence $(p_n)$ of primes where the ...
5
votes
2answers
288 views

Putting up the lights two

I hope you are familiar with this. Basically Each strand of 20 lights is wired like a 5x4 grid, and each bulb can be either blue, red, purple, or green. However, when you change the color of 1 ...
4
votes
9answers
1k views

Make 6 5 4 3 = 1

Can you find a way to make: 6 5 4 3 = 1 by concatenation and/or adding any of (and only) these mathematical operators: + - × ! ÷ ^ standard parentheses () You cannot add other numbers to the ...
4
votes
1answer
713 views

Points on a cube

Professor Halfbrain has spent his entire weekend by placing colored dots on the surface of a huge wooden cube. His objective was to find large groups of dots that form the vertices of a regular ...
4
votes
5answers
452 views

Determinant of Word Matrix

Challenge: Create a 3x3 matrix of letters (NO REPEATS) such that the determinant of the matrix forms words from the 'multiplications'. For example, in a simple 2x2 case, take the matrix $\begin{...
4
votes
1answer
372 views

答えはまた二桁の数字、その3 (The answer is another two-digit number, #3)

A colleague at work gives you a slip of paper at work one day, with symbols written on it: ・のいろ・はおに・・ みほくへ・やしと・ち ・ま・り・・・・・ぬ ・るゑ・ひ・・を・け もわ・かせふ・よ・・ ・・こた・え・・・れ ・そ・・・・・つて・ あね・な・・・・さら ・・・...
4
votes
3answers
458 views

Neighbouring numbers summing to a prime on a 3x3

Can you place distinct numbers from 0 to 9 on a 3x3 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Can you find multiple solutions? Note that the ...
4
votes
3answers
4k views

Solving a Rullo Puzzle

How can I solve in a (relatively easy) way, a Rullo puzzle? (Screenshot below) Rules: Enable or disable a circular number (pink is enabled) in order to make the row or column match the sum on the ...
4
votes
2answers
1k views

Another 6 tries to guess a number between 1-100

Inspired by 6 Tries to Guess a Number Between 1-100, how many guesses would it take if you can ask if the outcome of an operation is equal, less than, or more than a number. In other words, Alice ...
4
votes
1answer
267 views

A Hollow Sphere

Imagine a sphere with a hole that has been drilled clean through its center (i.e. a cylindrical piece of the sphere is now missing). This new shape, with the core missing, has height of 6 when ...
4
votes
2answers
656 views

Bridge building with irregular planks

Imagine you have a big rectangular pond in your back garden. You wish to build a bridge from your house in the lower left corner to the small pagoda in the top right. You have lots of planks of ...
4
votes
2answers
521 views

Lock Optimisation

In a simple combination lock, a sequence of several digits is used as a password, with one wheel per digit. Generally, it is not possible to unlock the lock without knowing the password, but due to ...
4
votes
2answers
407 views

5 weights on modified balance scale

This question is follow up version of What's the fewest weights you need to balance any weight from 0,5 to 40 pounds, on a modified balance scale with one arm twice as long as the other.   &...
4
votes
2answers
1k views

Unique Licence Plates

Note: This is a Mathematical puzzle, not a Mathematical problem. Although the answer could be solved with mathematics, lots of problems on Puzzling SE could be solved with mathematics, and the problem ...
4
votes
2answers
304 views

Alphametic with modulo

Solve this alphametic $ABCDEFG$ $mod$ $(A×B×C×D×E×F×G) = 0$ example : $ABCDE$ $mod$ $(A×B×C×D×E) = 0$ $13248$ $mod$ $(1×3×2×4×8) = 0$ Note : Do not replace any letter with 0. Each letter ...
3
votes
2answers
749 views

Rotating teams through stations

How can 14 teams rotate through 7 stations (2 teams at a station) without overlaps? NOTE: Every team participates in every station exactly once
3
votes
1answer
120 views

Keep the grid differences below $x$

Inspired by Keep the chessboard differences below eight Given an $n\times m$ grid of squares, what is the smallest possible integer bound $x$ for which it is possible to fill the squares with the ...
3
votes
2answers
935 views

Game against the Devil

While browsing through S.E you notice a spider crawl right out from under your keyboard! Startled, you twitch your hand and left clicked your mouse. You look up in shock as you notice that you just ...
3
votes
1answer
796 views

What movie am I?

The grid below contains the first part of a movie quote. What is the full 46-word quote, and what is the movie? Hint #1: Hint #2 Hint #3: Hint #4: Hint #5:
3
votes
2answers
222 views

A final incident in the flea circus: Part 1

The ringmaster of a flea circus draws a square $ABCD$ with corners $A=(+1,+1)$, $B=(+1,-1)$, $C=(-1,+1)$, $D=(-1,-1)$ in the Euclidean plane and picks a point $P$ with integer coordinates outside ...
3
votes
1answer
246 views

Hackers have created a new scheme to send passwords

Note: Following puzzle was used in certain competition and every detail of task is virtual (This certain competition is not ongoing). Hackers have created a new scheme to send passwords. ...
3
votes
1answer
226 views

Happy New Year?

Extend this infinite series by five more terms: 17, 3, 5, 7, 11, 17, 2, 3, 5, 11, 13, 17, 2, 5, 7, 11, 13, 2
3
votes
4answers
198 views

A curious incident in the flea circus

The ringmaster of a flea circus puts three fleas $A$, $B$, $C$ on three different numbers on the real number line, so that flea $B$ sits exactly in the middle between $A$ and $C$. Whenever the ...
3
votes
1answer
303 views

Theoretical Question - Rubik's Cubes

I have a very basic question on Rubik's Cubes. Take any completely solved cube or skewb. Now pick out (with hand) any two similar pieces and swap their positions, without changing positions/...