Questions tagged [number-theory]

A mathematical puzzle whose solution is heavily based on the arithmetic properties of the integers. General number theory questions are off-topic but can be asked on Mathematics Stack Exchange.

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-2
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2answers
157 views

The last digit for 3^(2019) [closed]

Which would be the last digit for $3^{2019}$ ? You can And afterwards
16
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4answers
1k views

What's in my pocket?

Well, I can tell you Johnny has memory cards in his pocket. Back Story My brother, Johnny, is a tech nerd. He loves gadgets of all kinds. As a matter of fact, you can be sure at any one given time, ...
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0answers
88 views

Maximize the Minimal Score [closed]

You are given 10 sets of papers with 10 questions each. Answer to each question is from 1 to 4. You somehow get your hands on the answer sheets and able to memorize each answer (Answer sheets only ...
9
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3answers
419 views

Number Guessing (Part 1)

I thought up two positive integers with product less than $500$. I told their product to Penny, and their sum to Sandy, and told both of them the constraints and they are both perfect logicians. ...
5
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1answer
2k views

How to programmatically solve math puzzle

I have this puzzle and I want to solve by code. I wrote simple code trying to brute force but it fail in one condition https://dotnetfiddle.net/cJyu3w Anyone know of a link or source how to solve ...
19
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1answer
993 views

Four mathematicians and their ages

Four mathematicians, none yet a centenarian, meet for coffee. The graph-theorist among them noticed that the common divisor graph of their ages (that is, the graph whose vertices are their ages, two ...
4
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1answer
132 views

Playing Collatz with graphs

a) Given a set of positive integers, its common divisor graph (CD-graph) is the graph whose vertices are the integers, two of which are joined by an edge if (and only if) they have a common divisor ...
9
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5answers
2k views

Nice no-computers way to find limerick primes?

A limerick number is a 5-digit number whose digits are in the form of a limerick rhyme scheme: $aabba$. How many limerick primes (limerick numbers which are also prime) are there? The answer is ...
11
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4answers
1k views

Professor Halfbrain and the number cycles

Yesterday afternoon I met professor Halfbrain at an art gallery. The professor looked tired and exhausted. He told me that he had spent many working days and many sleepless nights with lengthy ...
-6
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1answer
205 views

Puzzling set of numbers [closed]

Let's have the following numbers $23, 40, 42, 44, \sqrt{43},\ 128i, 130, \sqrt{172}\ $. What is the relationship between these numbers, taken four at a time? There are only two combinations when you ...
15
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6answers
637 views

A special triple of factors

Using each of the digits 1,2,3,4,5,6,7,8,9 exactly once, create three 3-digit numbers such that their product is a maximum.
5
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1answer
169 views

Generating special numbers [closed]

Here are three numbers that are related to one another: 9841, 8591, 4800 How are these numbers related and how are they generated?
11
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4answers
907 views

Making the whole set into primes

Let's say you start with a set of sequential integers starting from 2, so: $ 2, 3, 4, 5, \dots, N $ for some $ N > 2. $ The goal is to use identical basic arithmetic operations ($ +, -, \times, \...
6
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3answers
194 views

Find the value of $\bigstar$: Puzzle 10 - Uncertainty

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea, I recommend you solve Puzzle 1 ...
8
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3answers
634 views

Discover the six-character password!

You are given several pieces of paper which are as follows: (Unfortunately, a textual rendering is very difficult with this puzzle, so if someone can offer a suggestion on how to do it, that would be ...
0
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0answers
81 views

Hitting a car with a bullet [duplicate]

1) There is a road on which a car starts with an integral speed towards the left or the right, starting from an integral point (take the road to be the x-axis) 2) The speed and the point from which ...
7
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2answers
435 views

Smallest prime number which when spelt out contains the letters P, R, I, M, E

So inspired by recent slew of questions based on prime numbers. What is the smallest prime number when written out (Using the Western numbering system and English) would you encounter the letters P, ...
17
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4answers
3k views

Smallest PRIME containing the first 11 primes as sub-strings

In Smallest number containing the first 11 primes as sub-strings, @Alconja successfully found the smallest number which contains the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31) as ...
10
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4answers
715 views

Sharing cake among 9 or fewer people

You are expecting guests to your birthday party. You know that there will be at most 8 guests, but you don't know how many will actually come. What is the smallest number of pieces you should divide ...
9
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3answers
749 views

The Royal Mint of Alphagonia

In the Kingdom of Alphagonia nothing can be bought for less than 30 alphas, the local currency. 1) What three denominations of coins should the kingdom mint so that as many as possible of the (...
8
votes
1answer
559 views

Winning the Lottery

Bob: I hear you won the lottery. Alice: So I did! Bob: What six numbers did you win it with? Alice: Can't remember. All I recall is that they were all different, and none greater than 28. Bob: ...
10
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2answers
560 views

National Graph Lottery

In UK's National Lottery players choose 6 different whole numbers in the range 1 to 59, and win a large prize if all six match with the day's draw. Each choice of six numbers by a player gives rise ...
10
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2answers
594 views

A Magic Flying Saucer

Place 19 different positive integers on the vertices of this graph so that the 13 products of three numbers in a straight line are all equal. Do so in such a way that the product is as small as ...
11
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4answers
2k views

A Magic Diamond

Place 15 different positive integers on the vertices of this graph so that the ten products of three numbers in a straight line are all equal.
7
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0answers
239 views

What is a Freecell Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. If a word conforms to a special rule, I call it a Freecell Word™. Use the ...
16
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3answers
1k views

Box of tablets, whole or broken: solution required

This is a puzzle that I thought up whilst taking a course of meds. I currently haven’t solved it, and would be curious to know if anyone has a solution for it. Here goes: Scenario: John has a box of ...
6
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2answers
147 views

Positioning cards labeled with numbers from 0-9

Ann and Bob play a game. On a table there are 10 cards which are labeled with number from 0 to 9 each. Bob is allowed to change the position of the cards with a sequence of his preference. When he is ...
5
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2answers
128 views

A pile of chips involving powers of 2

Ann and Bob play alternately on a pile of chips. On each play, any number of chips, which is a power of 2 (including 1=$2^0$), can be removed from the pile. Obviously the number of chips to be removed ...
6
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1answer
175 views

A pile of chips involving primes

Ann and Bob play alternately on a pile of chips. On each play, either 1, 2 or 3 chips can be removed except if the number of chips is a prime number. In that case either 1, 2, 3, 4 or 5 chips can be ...
2
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2answers
191 views

How to find number of times sequence element $1$ is approached and from where?

Consider a sequence $1,-1,-1,-1,-1,-1,...,-1$. Start at the first element and move down the sequence according to the following rules: 1) If you jump from a $-1$ to another $-1$, turn the latter into ...
8
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2answers
755 views

IX-NAY on the IX-SAY

Will this sequence ever have a 6 in it? 9, 1, 1, 1, 10, 3, 1, 1, 10, 5, 1, 1, 10, 1, 5, 2, 1, 1, 10, 1, 1, 1, 5, 4, 1, 1, 10, 3, 1, 1, 5, 1, 1, 1, 5, 2, 1, 1, 10, 5, 1, 1, 5, 3, 1, 1, 5, 4, 1, ... ...
6
votes
1answer
220 views

I'm a Proper Divisor

Ann and Bob are playing a number game. Ann starts with the number 60. Then she subtracts a proper divisor of 60 from it. Bob then takes the number Ann made and subtracts one of its proper divisors ...
9
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4answers
547 views

The Football Squad

The sixteen players of a football squad, wearing shirts numbered 1 to 16, have arrived in town for a tournament. At their hotel, they are assigned 16 rooms consecutively numbered. Moreover, each of ...
12
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2answers
621 views

The Puzzling Reverse and Add Sequence

The sequence of numbers 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22,... (A056964 in the OEIS), in which the nth term equals n+reversal of digits of n, poses a number of intriguing puzzles. Here just ...
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0answers
78 views

Invert the numbers [duplicate]

I have an array of numbers containing 0 and 1 only and you are given a a constant C . You have to invert all the 0's to 1's by taking exactly C number of elements . What is the max number of 1's we ...
1
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1answer
208 views

Frobenius coin problem variation

Suppose you are give $n$ currency notes from $k$ to $k+n$ i.e $k, k+1,k+2.....k+n$ Where $k,n>0$ It's asked the total number of denomination of money that can't be formed using any number of ...
1
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0answers
61 views

How many ordered pairs (a,b) satisfy a^2=b^3+1, where a and b are integers? [closed]

(A)2 (B)3 (C)4 (D)5 I got 2 pairs (0,-1), and (3,2), but the correct answer is 5. Can somebody help? Thanks in advance!
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2answers
109 views
3
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2answers
464 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,...
4
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2answers
1k views

A king was born in a year that was a perfect square, lived a perfect square number of years, and also died in a year that was a perfect square

In which year could he have been born? (A) 1936 (B) 1764 (C) 1600 (D) 1444 The answer's (C). Why?
5
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4answers
882 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 ...
8
votes
1answer
403 views

Number sequence puzzle; 2, 10, 44 (+2 hints)

Predict the next three members of the sequence below and explain what the relationship is. 2, 10, 44, 1012, 248, This number sequence does not appear in the Online Encyclopedia of Integer ...
6
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1answer
139 views

Find the immediate square dancing neighbors, they dance together to perfect square

We live in a community of houses sequentially numbered from 1 to 100. We all love square dancing but only two immediate neighbors are joy to watch. If you concatenate their house numbers, it forms a ...
17
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2answers
2k views

We are two immediate neighbors who forged our own powers to form concatenated relationship. Who are we?

Our concatenated number is $ \overline{ABAC}, $ where $ A, B, C $ are all positive digits (1 - 9). Our relationship is $$ \overline{ABAC} = A^A + B^B + A^A + C^C $$ Who are we?
5
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2answers
213 views

SafeCracker #2 - The Mission Continues

Thanks to an alert StackE user, we were able to get the first safe open. Mission Details This next safe is in a former employee's house. He is gone for now, so we have no time to spare. We weren't ...
8
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3answers
652 views

Double or Take game

Double or Take is a two-player number game. Alice starts by selecting any positive integer. Bob's options are to: subtract a positive perfect square subtract a positive perfect cube, or double the ...
6
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2answers
1k views

Father and Son and Grandsons

The sum of the ages of a father, his son, and his two grandsons is 181. The father´s age has a common divisor greater than 1 with the ages of each of his three descendants, but not two of the latter ...
6
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2answers
335 views

Swap — A Puzzle I Created

This puzzle is called Swap. Let's find out why! Suppose you are given a random $\rm N\times N$ matrix (grid) with all the integers from $1$ to $\rm N^2$ each belonging in every grid square (a.k.a. ...
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2answers
238 views

What number + 1 equals itself? [closed]

Answer in numerical form. The answer is not an integer. The answer is in string form. The answer is not my love life...
7
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2answers
1k views

An Accountant Seeks the Help of a Mathematician

The accountant complaints to the mathematician: “I lent money to five other faculty members and still haven’t been paid back. You are one of them; the other four owe me 12 dollars altogether, but ...

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