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Tagged with eulerian-path contest-math
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Drawing the grid without lifting the pen
The below shape consist of $24$ segments with unit length. if we want to draw this shape without lifting the pen, what is the minimum length of the line we should draw?
$1)25\quad\quad\quad\quad\quad\...
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An ant walks on a cube over the diagonals of little cubes. Can it visit all little faces exactly once?
I have got this task at high-school math-contest seminar.
The theme is graphs.
Let us have $n \in \mathbb{N}$ and the cube $ n \times n \times n$. An ant can go over a diagonal of little cubes, but ...