For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions. Combinatorics is a ...

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13
votes
1answer
224 views
+50

Is it possible to uniquly number faces of a hexagonal grid with consecutive numbers

You have a grid of regular hexagons. The aim of the game is to have each hex contain the numbers 1-6 on its edges. Each edge must also be connected to another edge that has a value one higher and ...
0
votes
1answer
56 views
+50

Help with developing equation with combinatorial numbers

How can I get from $$k^{4} = a*\binom{k}{1}+b*\binom{k}{2}+c*\binom{k}{3}+d*\binom{k}{4}$$ to \begin{equation} k^{4} = \frac{(24a-12b+8c-6d)k+(12b-12c+11d)k^{2}+(4c-6d)k^{3}+dk^{4}}{4!} ...
3
votes
2answers
317 views
+100

Probability of some die face being missed N or more times in a row in M rolls?

Say I have a (fair) die with $F$ faces. I roll it $M$ times. How can I calculate the probability that some face was not seen for $N$ or more in a row of the $M$ rolls? (any face, not just a specific ...