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
1answer
678 views

I am caught when I was about to steal some candies

I am a eight years old boy, I love candies, but my mom does not want me to eat any more candies because I start to have black teeth :( but I still love candies so... Today when I was about to steal ...
3
votes
2answers
298 views

Pan Digital Lucky Seven wants you to figure out all the digits

$Given$: A, B, C, D, P, Q, R, S, T are distinct digits varying from 1 to 9. AB, CD, PQ, RST are all concatenated Numbers. From the given expression , figure out all the digits to make lucky seven. ...
24
votes
4answers
2k views

Savage Road Signs

There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker ...
2
votes
2answers
138 views

sum and gcd june19 challenge!

Can anyone please help me out with the https://www.codechef.com/JUNE19B/problems/SUMAGCD question? Chef has a sequence of positive integers $A_1,A_2, \dots, A_N$. He wants to split this sequence ...
5
votes
3answers
197 views

Find the Missing Members of this Powered Sequence

There are 4 missing members in this small series...labeled ???. Hint 1; Hint 2: Complete the series. $191$, $426$, $931$, $???$, $???$, $646$, $971$, $???$, $???$
11
votes
4answers
3k views

Use 1 9 6 2 in this order to make 75

I'm looking for a solution to make number $75$ with numbers $1$ $9$ $6$ $2$ in that order and the same rules as in Use 2 0 1 and 8 to make 67. Here a copy of those rules: You must use all 4 digits. ...
5
votes
2answers
155 views

Please figure out this Pan digital Prince

Given: P, R, I, N, C, E, T, O, M are all distinct digits varying from 1 to 9. PCRON, PRINCETOM are two concatenated numbers. PCRON is the highest possible number you can have fulfilling the ...
11
votes
2answers
527 views

2019 gold coins to share

You and your friend has found in total 2019 gold coins in a treasure hunt. Since your friend found the place to dig up, he deserves a bit more gold than you so you offer a game to share the coins to ...
4
votes
3answers
134 views

Make 2019 Factorial Multiplication a perfect square

N is not a square number and consists of 2019 factorial multiplication as shown below: $N=1!\times 2!\times 3!\cdots 2018!\times2019!$ At least how many factorial needed to be removed from the ...
2
votes
2answers
1k views

Finding numbers having exactly two distinct digits

We have $10^K$ road signs (numbered 0 through $10^K−1$). For each valid $i$, the sign with number $i$ has the integer $i$ written on one side and $10^K−i−1$ written on the other side. We need to ...
0
votes
1answer
128 views

Don’t let this daunting equation dissuade you to deduce the desired result

Given: A, B, P are distinct digits. AA, AAA, ABB are concatenated numbers. Relations: $$P=A+A+B$$ $$(AA + ABB)^P-(ABB)^P=(AAA - A) ^P+(B+B^B*B)^P+(B^B)^P$$ Don’t be afraid to make reasonable ...
4
votes
1answer
2k views

Finding Round Integer

An integer is round if it is greater than $0$ and the sum of its digits in decimal representation is a multiple of $10$. Find an optimal procedure to compute the $N^\text{th}$ smallest round integer. ...
3
votes
1answer
177 views

A Diophantine rational function [closed]

For how many integers $N$ is the rational function $\frac{N^2-2N-15}{N^2-N-12}$ also an integer?
3
votes
2answers
443 views

Let M and N be single-digit integers. If the product 2M5 x 13N is divisible by 36, how many ordered pairs (M,N) are possible? [closed]

Let M and N be single-digit integers. If the product 2M5 x 13N is divisible by 36, how many ordered pairs (M,N) are possible? -- source I tried it by reducing 36 into its positive factors (1,2,3,...
2
votes
1answer
219 views

Mathematical Sequence Based on Prime Numbers

This sequence is based on prime numbers Hint 1: 16, 17, 11, 16, 10, 8, 13, 7, 14, 8, 11, 7, 5, 10, 4, 11, 5, 10, ?, ?, ? What are the final three numbers?
3
votes
0answers
182 views

Magical Evening

Tonight will be a magical evening full of fun and excitement if you can figure out this riddle. When the clock strikes nine but loose three dash you will find a feast at the seven of these. Where ...
-5
votes
3answers
227 views

From the given Square - Factorial Relationship, deduce the unknowns

$Given$: A, B, C, D are distinct digits and can vary from 1 to 9. DB is a concatenated number. From the following relationship, solve for A,B,C,D. Give your deductive reasoning. Please read all ...
4
votes
2answers
562 views

Find the Factorial From the Given Prime Relationship

$Given$: $P$, $Q$, $R$ are three distinct Prime Numbers $P!$ = $Q$ x $R^Q$ x $P$ Find P, Q, R.
33
votes
9answers
4k views

Winning Strategy for the Magician and his Apprentice

There are $13$ upside-down opaque cups and $2$ balls, a magician and his apprentice and yourself. You decide under which cups to put the balls, and the objective of the magician is to find the two ...
2
votes
1answer
208 views

Deduce the Component Digits from these three Sets of Symmetric Power Relations

Use calculator to the minimum. Under Logical Deduction, these Daunting Relations will quickly melt away to reveal the constituent digits. All three sets show beautiful symmetric Relations with first ...
6
votes
5answers
354 views

Shortest time to meet

Three runners are located at the corners of an equilateral triangle, 100 meter a side. They run to a point inside the triangle and their goal is to do it as fast as possible. If they run at the same ...
0
votes
1answer
347 views

Why is “D” the Center of “Attention” at this Circular Conference

All the Alphabet Guests are seated according to their order at a unit distance apart around this circular conference table. Why is “D” the center of “Attention”?
1
vote
1answer
99 views

Devil goes Pan Digital..Sometimes Lucky..Sometimes not..Figure him out

$Given$: D, E, V, I, L, G, N, O, T are distinct digits (1 to 9). $D+E$ brings good luck $I+L$ is unlucky $N+O-T$ is unlucky too. $DDDD$ = $(D+E)^V$ + $(I+L)^G$ + $(N+O)^T$ Fully Figure out ...
-2
votes
1answer
147 views

What is next: 2, 3, 5, 13, 89, 233, …? [closed]

Based on what is shown, what is the next number in the sequence?
3
votes
5answers
154 views

3 as a Sum of 3 Pan Digital Expressions [closed]

$Given$: $3$ = { A } + { B } + { C } Where A, B, C represent 3 unique Pan Digital Expressions. Each contains all the digits 1 to 9 occurs only once. Expressions contain only plus, division ...
-10
votes
1answer
165 views

Starting with e and Pi…how do you get to Phi? [closed]

No equations...need one line answer only. No tricks here.. $e$, $\pi$, $\phi$ are regularly used universal constants. Here is the one line answer: If you want, you can do more to improve accuracy ...
19
votes
2answers
2k views

Diet Coke or water?

At PuzzlingCorp, all employees have a break at 10:00am sharp every day, and immediately proceed to get either plain water or a diet coke. The people at PuzzlingCorp are also highly susceptible to ...
2
votes
1answer
74 views

Express 2222 as a sum of 3 powers in 2 Different Pan Digital Expressions

Solve for the digits in this Unique set of Palindrome- Pan Digital Expressions: $2222$ = $(A/B)^C$ + $(D/E)^F$ + $(G/H)^I$ $2222$ = $(A/B)^I$ + $(D/E)^F$ + $(G/H)^C$ Where, A,B,C,D,E,F,G,H,I ...
1
vote
2answers
63 views

Rep Digit Palindrome expressed as a Unique set of Pan Digital Relations

Allowed Operations: Addition, Subtraction, Multiplication, Division, Exponentiation. Right and Left Bracket use permitted. Express $2222$ In $2$ Different ways using all the digits 1 to 9 only ...
2
votes
3answers
120 views

Express the Squares of first 20 Numbers with only numbers found in their Sum of Digits

Allowed Operations ...Addition, Subtraction, Multiplication, Division, Exponentiation, Simple Factorial. Left and Right Brackets allowed. Expression should involve minimum number of total characters: ...
8
votes
6answers
829 views

Restoring order in a deck of playing cards (II)

Michelle has a deck of 52 playing cards in a pile with their backs facing up. She takes the first 2 cards in the pile, turns them over, and places them at the bottom of the pile. She now takes the ...
7
votes
1answer
200 views

Make a formula to get the highest score

In this puzzle you need to obtain the highest score with the following rules 1) choose two digits from 1, 2, 3, 4, 5, 6, 7, 8 and 9. These digits are represented by two letters, let us say $T$ and $M$...
24
votes
2answers
479 views

The mysterious operation $\oplus$

We are given an operation $\oplus$ that is associative and commutative, has $0$ as a neutral element, and we know: $1/10 \oplus 1/6 = 5/29$ $1/6 \oplus 2/3 = 7/10 $ $1/5 \oplus 2/5 = 3/7 $ $1/4 \...
-4
votes
1answer
128 views

Simple Rule Generates this Sequence from Well Known Number Series

First 6 terms generated on applying the simple rule are displayed here. 5, 8, 18, 102, 322, 1830, ?, ?, ? Hint 1: Hint 2: Hint 3:
-5
votes
2answers
137 views

Numberless Sudoku with Just a Letter and Symbol Combination

A Standard 9x9 Sudoku uses the digits 1 to 9. You are only allowed to use a single letter(say T) and a symbol of your choice to represent the digits 1 to 9. Rules should be well defined and the ...
5
votes
2answers
166 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 ...
13
votes
3answers
2k views

Restoring order in a deck of playing cards (I)

Michelle has a deck of 52 playing cards, stacked in a pile with their backs facing up. She takes the first 2 cards in the pile, turns them over, and places them at the bottom of the pile. She now ...
5
votes
4answers
869 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 ...
3
votes
1answer
222 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
9
votes
3answers
603 views

A Mathematical Discussion: Fill in the Blank

I originally saw this on r/puzzles, and thought it deserved a place here. I have a solution to this puzzle, but it's really long and ugly. If anyone comes up with something simple, please share! ...
7
votes
2answers
230 views

A Guide to the Number Rotation Puzzle

This is an extension of What is the strategy to solve Simon Tatham's Twiddle? in that it explicitly goes beyond the default gamemodes of Twiddle The Number Rotation Puzzle (NRP) is a combination ...
12
votes
1answer
385 views

Infinite Sequence based on Simple Rule

Using one simple rule, an Infinite Sequence has been developed. First 30 terms are given. Can you continue the sequence for at least next Ten Terms? Series continues from top left to bottom right. $...
0
votes
1answer
75 views

We are Unique Friends. Our Special Squares Share a Common Bond…Figure us out

Use logical deduction only and document your steps in detail. $Given$: A, B, C, D, E, F, M , T are distinct digits(0 to 9). ABC, EBF, DDABC, MCMABC, TBBB are all concatenated Numbers. $...
32
votes
6answers
6k views

Why is this Simple Puzzle impossible to solve?

Connect each red circle with each black circle by drawing a line and the lines should not touch. From each red circle, 3 lines must be drawn which connect red circles with black circles, but the lines ...
0
votes
1answer
115 views

UVC wants to give you a Helping Hand in Solving these Unique Set of Pan digital Fractional-Decimal Relations

Use pure logic and deductive reasoning only. Document detailed steps in arriving at final solution. You can use calculator minimally. $ Given$: Utilizing These two unique set of Pan digital ...
3
votes
2answers
143 views

Devil in Different Disguises but in Prime Shape…Can you Figure out his Diverse Expressions?

$Given$ $Devil$ goes by $666$ Express him as 1). Sum of all Primes in 3 Different ways using all the digits 0 to 9. Use only + sign. 2). Sum of all Squares of Primes. Use only + and ^ signs. 3)...
12
votes
4answers
853 views

Find the three digit Prime number P from the given unusual relationships

$Given:$ P is a 3 digit prime number Q,R,S,T are distinct digits( 0 to 9 ) QRS is a concatenated number $Relationships:$ $P$ = $QRS + T$ = Reverse of $( QRS * T)$ Find P using just ...
-1
votes
3answers
310 views

WAS IT A CAT I SAW? Do Some Detective Work & Catch The Imposters

Carolina County Community Cat Conference is going on at a resort exclusively reserved for Prime Members. Some look-alike impostors, aka cats, have sneaked in. They all wear fancy name tags that ...
-1
votes
2answers
120 views

Famous Number Displays Dual Cubic Relationships..Figure it out

$Given$: A, B, C, D are all distinct digits. ABCD is a concatenated number $ABCD$ = $A^3$ + $(A+C+D)^3 $ = $D^3+ (A + D)^3$ Figure out this Number and why is it Famous? Also provide ...
6
votes
5answers
324 views

How to Modernize Student Council

You are the math teacher at a high school and you are in charge of organizing Student Council for the whole school next year. Your boss, the Principal, read a research paper on Student Councils and ...