# Tagged Questions

57 views

### Sum of possible permutations

Lets call two arrays A and B with length n almost equal if for every i (1 <= i <= n) CA(A[i]) = CB(B[i]). CX[x] equal to number of index j (1 <=j <= n) such that X[j] < x. For two ...
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### Count swap permutations

Given an array A = [1, 2, 3, ..., n]: ...
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### Combinations and Permutations. integer solutions [closed]

(a) How many integer solutions are there to the equation $x + y + z = 15$ if (i) $x$, $y$, $z$ are non-negative? (ii) $x$, $y$, $z$ are positive? (iii) $x$, $y$, $z$ are non-negative and $z \leq 5$? ...
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### How many of these numbers are divisible by 4?

There is this question that I have no idea where did I make the mistake. Each of the digits 1,1,2,3,3,4,6 is written on a separate card. The seven cards are then laid out in a row to form a 7-digit ...
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### Filling in blanks in a multiplication problem knowing only the set of digits in the product and that 9 divides each factor

The 5774 Ulpaniada (part 2 of it) includes the following question: The following multiplication exercises uses all $9$ digits $1,2,3,\ldots,9$. The digits are encoded by asterisks. We are told ...
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### Number of ways in which a composite number can be resolved into 2 coprimes? [duplicate]

for example 210 = 2*3*5*7,number of relative primes is 2*(4-1) =8,please help me derive this result.here's my try = 4C0+4C1+4C2+4C3+4C4=2*4 .Since nCr = nCn-r we decide this by two.4C0 couples with ...
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### Distribute Gifts among students

$N$ students are to be provided with gifts We know that the $i$'th student wants to get at least $a_i$ gifts. The teacher wants to give distinct gifts meaning if he give $x$ gifts to one student then ...
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### Numbers permutation

Given $n$ numbers and $k$ positions I want the total number of permutations of these n numbers on these $k$ positions if repetition is allowed and if the following two arrangements are considered ...
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### Number of ordered pairs $(x,y)$ with $x,y \in \{ 1, \dots, N\}$ such that sum of numbers in pairs is divisible by $k$?

Given $N$ and $k$. Find the number of ordered pairs $(x,y)$, with $x,y \in \{ 1, \dots, N\}$ such that sum $x+y$ is divisible by $k$. and x less than y. example $N=10, k=4$ answer = $10$ Pairs- ...
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### Show that the function $p(k)=k+(-1)^kc$ is a permutation of the set of all integers

This problem is from the book "Concrete Mathematics (2nd) written by Graham, Knuth and Patashnik" Show that the function $p(k) = k+(-1)^kc$ is a permutation of the set of all integers, whenever ...
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### Is there a formula in permutations and combinations if we are to find the sum of number of 1's in binary expansion of a number from 1 to n

We are given $N$. Suppose $f(x) =$ number of $1$'s in the binary expansion of $x$. We have to calculate $f(1) +f(2) +f(3)+ \dots +f(N)$. So is there a formula for this sum directly in terms of ...
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### How many solutions are there to $abc+def=ghi$, where $a,b,\ldots, h,i$ are distinct non-zero digits?

I saw this problem posted by Google. Those posting in the comments found solutions using computer programming. I would like to know if there is an easier solution than trying every single combination. ...
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### “Randomize” output of a Linear Feedback Shift Register for the same taps?

I'm using a (Galois) LFSR to sample a large array, ensuring that each entry is only visited once. I simply skip past the entries that exceed the array length. With the same taps then the array entry ...
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### How many permutations are there from x bits to y bits?

Can you have a permutation function where the size of the domain isn't the size of the range? I know the number of permutations from x bits to x bits is $2^x!$, but if you can permute x bits to y ...
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### Total number of ways to arrange the prime divisor of a number so it can be written using M digits

How many ways we can arrange all the prime divisor of a number so it can be written using M factors, where M <=T. T is the total number of prime divisor of the give number N. Example:N=27, its ...