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.

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0
votes
1answer
51 views
+50

Probability of hitting a number $Ib$ (rare case)

Consider a set $S$ of $N^{3/2}$ numbers. Fix a collection $T$ of $N^{\frac{1}{2}}$ numbers. With every trial, we have the freedom to choose $N^{1-\epsilon}$ of them at a time without overlapping. My ...
7
votes
1answer
135 views
+200

Smallest integer $k$ so that no Sudoku grid has exactly $k$ solutions

Inspired by this question, consider hints on a Sudoku board. A regular puzzle has a unique solution. It is clear that there are puzzles with 2 or 3 solutions, and therefore, I guess, puzzles with say ...
3
votes
2answers
90 views
+100

find a group of lowest N numbers so that no 2 pairs have the same bitwise or

I am trying to find the lowest group of N numbers (i.e. N=1000) so that no 2 pairs from the group have the same bit-wise or. more specific need to find a group $A = \{a_1,a_2,a_3,..,a_N\} $ such ...