# Tagged Questions

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### number of derangements

In the normal derangement problem we have to count the number of derangement when each counter has just one correct house,what if some counters have shared houses. A derangement of n numbers is a ...
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### How is the algorithm for recursively printing permutations of a set of numbers this equation our professor gave us?

I'm having a great amount of trouble understanding where my prof got $T(m, n) = n(T(m+1, n-1) + m+1 + n)$ if $n > 1$ as the recursive formula for the algorithm for recursively printing the ...
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### all possible sequences of positive integers that sum upto N and are strictly increasing

I have $N$ bricks and i have to build a staircase. A staircase will consist of steps of different sizes in decreasing order, no two step size should be same. Each step should consists of atleast one ...
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### Who invented the breadth-first permutation algorithm?

My initial problem was solved here. It is about enumerating all n-tuples of a permutation in a specific order. The solution algorithm is very simple and I'm sure has been used before. However, I did ...
I know this is an extremely noob question, but I need some help. since I am stuck Prove the formula $$p(n,r) = \frac{(n + 1 -r) \; (r^2 - 3r + 3) \; (r-2)!}{n!}$$ from this answer.