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.
197
questions
5
votes
2answers
108 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 ...
1
vote
0answers
48 views
Determined the missing items
The two distinct sets of numbers below exhibit a pattern from the same kind, similar,but at the same time somewhat contrasting and a bit different to each other,one set is complete, the task is to ...
3
votes
0answers
96 views
How to find number of times sequence element $1$ is approached and from where?
Suppose i have sequence 1,-1,-1,-1,-1,-1 ........-1 .Now i start jumping from first sequence element (i.e 1 in this case) to next one .If i jump from 1 to -1 then element -1 will remain as it is.if i ...
8
votes
2answers
726 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
200 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
votes
4answers
521 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
votes
2answers
592 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 ...
0
votes
0answers
71 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
vote
1answer
204 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
vote
0answers
55 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!
-1
votes
2answers
75 views
If $a$ and $b$ are two odd distinct prime number and if $a>b$, then $a^2-b^2$ can never be divided by [closed]
(A) 13
(B) 11
(C) 17
(D) None of the above
3
votes
2answers
441 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
votes
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
votes
4answers
866 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
339 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
votes
1answer
138 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 ...
18
votes
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
votes
2answers
197 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
votes
3answers
628 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
votes
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
votes
2answers
312 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. ...
-7
votes
2answers
175 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
votes
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 ...
19
votes
4answers
759 views
Consecutive integers around a circle
Find a block of positive consecutive integers that can be placed around a circle in some order so that any two adjacent numbers always have a common divisor greater than 1.
8
votes
5answers
646 views
The Legend of Four
As far as I know, all numbers have a root of 4. What I mean by this is as follows:
Starting with any number, for example 384, I take the number of letters in that number. Then I repeat this process ...
13
votes
2answers
718 views
Digit sums of successive integers
For a natural number $x$ both, the digit sum of $x$ and the digit sum of $x+1$ are multiples of $7$. What is the smallest possible $x$?
2
votes
2answers
365 views
Can the sum, difference and product of 2 numbers be perfect squares? [closed]
If we take 2 numbers $x$ and $y$ such that $x>y>0$ and , can $x + y$, $x - y$ and $xy$ all be perfect squares?
3
votes
2answers
86 views
Can you have the harmonic, geometric, arithmetic and quadratic mean of 2 numbers all being integers? [closed]
I created this problem looking at the hm-gm-am-qm inequality (hm = $\frac{2xy}{x + y}$, gm = $\sqrt{xy}$, am = $\frac{x + y}{2}$, qm = $\sqrt{\frac{x^2 + y^2}{2}}$ and hm $\le$ gm $\le$ am $\le$ qm).
...
11
votes
4answers
4k views
Create the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!
Inspired by the last year's "2018 four 4s challenge", I thought it's time to welcome 2019 by a similar challenge. This time you have to use the digits 2, 0, 1, 9 in this particular order to create the ...
4
votes
8answers
531 views
Finni's tricky game
Finni’s game:
Person A thinks of a number (1 to 10). This number is called n.
Person B says a number (1 to 10). This number is called x.
Person A tells the absolute difference of n and x. This ...
3
votes
1answer
153 views
Three-digit multiplication puzzle, part III: Return of the Hex
Followup to: Three-digit multiplication puzzle and Three-digit multiplication puzzle, part II: ever heard of senary?
Place different three-digit hexadecimal numbers (000-FFF) on each of the seven ...
3
votes
2answers
143 views
Three-digit multiplication puzzle, part II: ever heard of senary?
Followup to: Three-digit multiplication puzzle
I'd never heard of "senary" either, until creating this series of three puzzles. It seems that "senary" is the word for base-six notation. Who knew? ...
4
votes
1answer
190 views
Three-digit multiplication puzzle
Place different three-digit numbers (000-999) on each of the seven nodes of the following diagram:
There are six lines in the diagram, on each of which are three of the nodes. On each of those lines, ...
7
votes
1answer
505 views
Fourteen numbers around a circle
Place the numbers 1 to 14 around this circle so that both the sum and (absolute) difference of any two neighboring numbers is a prime.
6
votes
2answers
311 views
The Magic Letter H
Place seven different positive integers on the empty disks of the H figure below so that the product of the three numbers in any straight black line is always the same. Now place seven other numbers ...
14
votes
1answer
744 views
My Social Security Card Number
I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit ...
9
votes
2answers
1k views
Ten-digit number that satisfy divisibilty rules for 2,3,4,5,6,7,8,9,10&11
Question:
Arrange the digits 1,2,3,4,5,6,7,8,9,0 to make a ten-digit Number that satisfies all of the divisibility rules for 2,3,4,5,6,8,9,10,&11. BONUS: make the number also divisible by 7
-5
votes
1answer
77 views
What is the pattern that describes these numbers? [closed]
Supposed you are given the following numbers:
6
28
496
8128
33550336
8589869056
What's the relation between them?
6
votes
8answers
521 views
Make $1,\dots,15$ using $3, 9, 9, 9$
This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post.
Can you find a way to make all the natural numbers ...
61
votes
24answers
19k views
Make 0 0 0 0 = 8
Can you find a way to make:
$0\ 0 \ 0 \ 0 = 8$
by adding any operations or symbols? You can use only these symbols:
$+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$.
It is limited to this list, and ...
7
votes
3answers
215 views
Is this number unique?
Inspired by Interview Question or Pathbreaking puzzle and A121808.
Start with $1$, and count the number of times $1$ occurs, and report this in the format 'number of ones:1', i.e. the next term is $...
10
votes
6answers
2k views
Maximize the number of factorials in your solution to 6 5 4 3 = 1
Using the same rules as Make 6 5 4 3 = 1, but maximize the number of factorials. You may not take the factorial of 1 or 2.
This is harder than it looks. A great answer has six factorials, an ...
11
votes
11answers
10k views
Make 6 5 4 3 = 81
Can you find a way to make:
6 5 4 3 = 81
by concatenation and/or adding any of (and only) these mathematical operators:
+
-
×
!
÷
^
standard parentheses ()
You cannot add other numbers to the ...
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 ...
22
votes
10answers
14k views
Make 5 5 5 5 = 19 [closed]
Can you find a way to make:
$5\ 5 \ 5 \ 5 = 19$
by adding any operations or symbols? You can use only these symbols:
$+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$.
It is limited to this list, and ...
0
votes
2answers
202 views
6
votes
1answer
326 views
Math Puzzle - What am I?
I am X. I was roaming around some place and found another X. We got attracted. Got into some operation and generate Y.
Me and my X got together now and went to roam the places.
We found the group ...
8
votes
3answers
487 views
Do they have to be integers? [closed]
$A^2$ + $B^2$, $AB$, and $A + B$ are all integers.
Do both $A$ and $B$ have to be integers? If not, what is an example where they are not?
3
votes
1answer
185 views
A football tournament
During a tournament, seven football teams, three European, three South American, and one from Africa, scored a total of 89 goals.
The number of goals scored by the African squad was relatively prime ...
22
votes
1answer
735 views
A Tour Around a Triangle
Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add ...
