Questions tagged [mathematics]

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

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68 views

Show that : $n =E(n*LOG((10*n)/(1+n))+1)$, $n> 0$, n integer? [closed]

Show that $$n =E(n*LOG((10*n)/(1+n))+1)$$ for $n> 0$ , $n$ is integer and E integer part(The ENT function on excel).
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100 views

Even and primes puzzle?

this is secret numbers that increase regularly, what is the order? If you like numbers, it will be fun. $2^3 \times224299$ $2^2 \times 3^2 \times 19 \times 3557$ $2 \times 5 \times 320647$ $2 \times ...
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39 views

How to reconstruct the explicit form of a function? [closed]

There is a function $f(x,y)=z$, and $2\cdot x<y$; $x, y, z \in N$ such that $f(x=2, y=5)=32$ $f(x=2, y=6)=36$ $f(x=2, y=7)=40$ $f(x=3, y=7)=48$ $f(x=3, y=8)=52$ $f(x=3, y=9)=56$ Question. Can ...
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3answers
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77-digit number divisible by 7 with seven 7s

The smallest number divisible by 7 with seven 7s is trivially 7777777. Then, what is the greatest 77-digit number divisible by 7 which contains seven 7s?
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6answers
3k views

Logical puzzle from a math homework for Russian fifth-year school students

The daughter of a relative of mine, a fifth-year school student in Russia, got the following math homework from her teacher: Here's my translation: Logical task No. 26. Students were solving a task ...
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1answer
138 views

NSE iq test please teach me [closed]

http://free.ultimaiq.net/nse.htm 35, 147, ?, 2387 357, 1251, 152, ?, ?, 0 452801, 773924, 102410, 471056, ? 011010, 100010, 100010, 100010, 000010, ?, 100010 1001, 4524, 4299, 3984, ? 91420512, ...
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168 views

A robot moving on a grid. Part 2

This is an extension of the discussion A robot is placed on a grid point. At each move the robot must take three steps along the edge of the grid. After each step the robot must turn right. Lengths of ...
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1answer
214 views

Kaboom-y numbers!

Here is a new type of puzzle poem I made. Enjoy! Note: The title is named like that for a reason. I have a number in mind, it is super cool, But there's something you need to know, or you will find ...
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1answer
118 views

Unusual connections of numbers

Let's have the equation $(DX)^2-Y^2= ± Z^5$ and $x,y$ two positive integers greater than zero. From some facts we can obtain solutions of the above equation by giving integer values at $x,y$. Examples:...
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4answers
255 views

Express numbers 1 - 100 using only 1, 2, 3, 4

The least number that cannot be written using the numbers 1, 2, and 3, each exactly once, and any combination of standard arithmetic operations (including factorials) is 41. What is the least such ...
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3answers
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Using pi and tau [closed]

Only using /pi and /tau (2pi), make as many numbers as you can from 1 to n, where n is a whole number. Restrictions: You can use basic operations such as +,-,*,and /. You can also use operations ...
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2answers
113 views

Houses on a street, a 1914 puzzle

Srinivasa Ramanujan was said to have answered this riddle almost immediately when brought to his attention by Prasanta Chandra Mahalanobis, taken from a December 1914 print of The Strand Magazine: He ...
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0answers
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Problem Solving [duplicate]

Long time ago in Egypt, an old man died and left a herd of 41 camels to his three sons. According to his will, the oldest son should get 1/2 of the camels, the second son 1/3, and the youngest 1/7 of ...
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4answers
400 views

Buying weight plates for a home gym, what is the fewest number I need

I'm buying a home gym set-up for my son (really!) and I want to know the fewest number of weight plates I need to buy to be able to go up in 5kg increments to 170kg. The bar weighs 20kg and the ...
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1answer
50 views

100 lightbulbs in a room [duplicate]

There are 100 lightbulbs in a room, each with it’s own switch in the off position (all lightbulbs work and start off, no funny business). There are also 100 people numbered from 1 to 100 standing ...
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1answer
224 views

The ID of my next Zoom meeting

My friend is inviting me to a Zoom meeting. Rather the sending me the ID for it, he sent me the following 10 IDs. "Each of these numbers has precisely two digits which are identical, and exactly ...
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86 views

Math Puzzle #01 (remade from Math Tapestry Puzzle) [closed]

Transcription: Make a pair (a, b) such that a is a 1 by 1 square and b is a square formed by two adjacent quadrants. You may not repeat a number. Make the pair as small as possible (albeit make it ...
9
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2answers
321 views

Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
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2answers
148 views

Coffee theorem puzzle [duplicate]

I am back yet with another puzzle, my last one was made this morning, and this one is a copied one from an app/website called Brilliant. So, this is especially for those who do not have Brilliant ...
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3answers
270 views

Back at the PSE headquarters

Roaming through the PSE building I come across a solid steel door. Above the door is a sign saying “Astrodome R”. I had no idea this place delved into astronomy. Below this sign is a painting of sorts:...
6
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2answers
218 views

Recreational checkers problem

Alberto places N checkers in a circle. Some, perhaps all, are black; the others are white. (The distribution of colors is random.) Betiil places new checkers between the pairs of adjacent checkers in ...
5
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1answer
139 views

Unusual number triads

Let's have the following equations. $1388^2+803^2=137^3$ $236^2+115^2=41^3$ $666^2+413^2=85^3$ As you can verify by visual inspection the numbers of each triad have (GCD)=1. Question 1) How can we ...
8
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3answers
416 views

An infinite number of special roots?

You may: Reduce a number by dividing it by its number of prime factors, counting multiplicities. Repeat this on the result as much as you want. Is there an infinite number of squares that can be ...
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1answer
75 views

Find me 5 very special squares

I forgot a requirement in my previous question (Find me 5 special squares) I am afraid now that this one is too simple/similar, but this was what I actually intended: There are many squares that ...
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1answer
117 views

Find me 5 special squares

Assumption: There are many squares that cannot be written as a number divided by the number of prime factors of that number. Can you give me $5$ of such squares that are relatively prime? (Example: $...
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1answer
234 views

Slim at any size?

Recall from ŧhis question that we call a positive integer slimdownable or slim for short if it is part of a sequence of integers where each is followed by itself divided by its length, i.e. its number ...
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4answers
290 views

876925431=2016 Use the four basic operators

Use the four basic operators ×, ÷, +, − and if you want brackets to make: 8 _ 7 _ 6 _ 9 _ 2 _ 5 _ 4 _ 3 _ 1 = 2016. You can use each operator as many times as needed. Concatenation is not allowed.
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5answers
2k views

Slimming down integers to a single digit

Slimming down an integer is dividing it, when possible, by the number of its digits. Thus, 315 slimmed down becomes 105, whereas 316 cannot be slimmed down. There are a few numbers that can be ...
5
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2answers
280 views

General orchard planting problem for circles

My previous puzzle asked for the maximum number of 4-point circles attainable from a configuration of $n=10$ points drawn on a plane. I am now interested in generalizations of this puzzle to arbitrary ...
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2answers
113 views

Mathematical sequence puzzle

Bob is trying to crack a puzzle. He finds this numerical sequence: 9056, 528, 64 What should he input after 64?
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1answer
251 views

Largest range of consecutive integers that can be formed

Using a 10-element multiset of $\{1, 2, 5, 10, 20, 50, 100\}$, what's the largest range of consecutive integer values that can be produced (note that $0$ isn't counted)? For example, I could take ten ...
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1answer
64 views

Finding missing number from a table [closed]

This is a brainteaser I recently encountered: Find the missing number in the table: $$\begin{array}{|c|c|c|c|} \hline 26& 6 & 5 & 4 \\ \hline 13 & 3& 2& 5\\ \hline 25 & 7 &...
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176 views

The meaning of the related numbers

Question: What follows in the sequence below? 10233432943 As a hint, I must say I do not like the single 1 in it. It is unclear if the sequence even started with 1, but the 1 it needed. I had to ...
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3answers
774 views

Flipping coins in a circle

We have a set of N coins that are all placed in a circle. They all have "Tails" as their face up side. The coins are all distinct and have numbers (1,2,3...N) written on them. In each move, ...
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2answers
125 views

Squares related to circles [closed]

Fibonacci numbers, circles, squares; everything is connected in the digital world. Can you make two squares from a circle? Seven decimals should be accurate enough. Which two numbers am I seeking? I ...
4
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1answer
131 views

Orchard planting problem for squares

The classic Orchard planting problem asks for the maximum number of 3-point straight lines attainable from a configuration of $n$ points drawn on a plane. Here we are interested in a variant of this ...
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3answers
423 views

Orchard planting problem for circles

The classic Orchard planting problem asks for the maximum number of 3-point straight lines attainable from a configuration of $n$ points drawn on a plane. Here we are interested in a variant of this ...
0
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0answers
101 views

Formula for the sequence 1, 1, 1, 21, 3, 1, 4, 1, 5, 1, 6,

The sequence 1, 1, 1, 21, 3, 1, 4, 1, 5, 1, 6, ... appeared in one of my tutorial sheets in 2019. I assumed that the fourth term, 21, was a mistake (was supposed to be ..., 2, 1, ...) then it made ...
5
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2answers
159 views

Highest n where an equal number in all cells is (im)possible

Inspired by Board with all 2020s : Zeroes are written in all cells of a n×n board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it. ...
2
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1answer
95 views

Making *9* congruent triangles from the pieces of a triangle dissection

Working on the making 7 congruent triangles from the pieces of a triangle dissection question I realized it's possible to do even better! So here it is for extra points: Use six lines to cut a ...
5
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1answer
128 views

Accomplice numbers

The reverse of a number is the number obtained by reading the initial number from right to left: for example, the reverse of 125 is 521. Two integers are said to be accomplices when these numbers are ...
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2answers
154 views

How many steps for matchstick-Lychrel numbers?

The Lychrel number is famous in the recreational mathematics. The process about the Lychrel numbers reverses arrangement of the previous number. Mimicking Lychrel numbers, I would like to devise ...
9
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5answers
926 views

Two player Monty Hall variation

Alice and Bob are going on a game show as partners. In this game, there are three doors, which contain a car, the car keys, and a goat, which are arranged randomly and secretly behind the doors. Alice ...
4
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1answer
325 views

Does “naked set” method always solve a sudoku?

Is always possible to solve a sudoku (that has a unique solution) using only naked pair/triple/quad methods? If not, what about using naked set and hidden set methods combined togheter? I need to know ...
8
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1answer
206 views

Each fruit is a combination of two elements

Hello Puzzling community! Here's a simple pattern question I created recently: 1) Apple = 50 X 2) Banana = 33 G 3) Cherry = 77 Y 4) Dragon Fruit = 137 G 5) Elderberry = ...
3
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1answer
167 views

Lazy Box Sorting

In front of Louis there are 10 boxes containing different foods: tomatoes, (red) herrings, and bananas. The boxes are arranged side by side in a line. Right next to the last box are three bigger ...
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5answers
1k views

Board with all 2020s

Zeroes are written in all cells of a $5 \times 5$ board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it. Is it possible to obtain ...
4
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6answers
389 views

Thick as two short planks

That didn't go to plan. You just wanted to help your friend the artist redecorate. In the process you mananged to make an ugly notch in their favorite table, scratch their wall when moving said table ...
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4answers
1k views

A bet with your friend

James, your friend, has invited you to bet with him. He has a fair die, with $3$ faces showing $0$ and $3$ faces showing $1$. You pay him $\\\$70$. He throws the die $15$ times, and records the sum of ...
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0answers
127 views

The Game of Numbers (#02)

Related to The Game of Numbers (#01) Agatha just decided it still isn't enough because she thinks it's way too easy. She decides to add one more rule to the list and change some of the existing rules. ...

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