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Results tagged with puzzle
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user 9025
Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.
1
vote
Fill the board with zeroes, inverting the intersections of rows and columns
This is an extended comment short of a solution.
Define an $n^2\times n^2$ matrix $A_n$ with rows and columns indexed by the positions $(i,j)$. Row $(i,j)$ of the matrix is 0 except for 1 in the col …
- 37.7k
9
votes
Probability of a black path on a random chess board
James correctly identified percolation theory as the place where something like this is studied seriously. But let's do an elementary calculation.
Each possible path consists of $4n-1$ squares and i …
- 37.7k
13
votes
Puzzle on deleting k bits from binary vectors of length 3k
Here is an exponential lower bound. We begin by determining exactly how many strings $Y$ of length $n$ can be reduced to a given string $X=x_1x_2\cdots x_k$. In general $y$ might contain many copies …
- 37.7k