Problems for the week!

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    Ashani Dasgupta

    Here are three problems for your brain!


    Can you glue edges of an octagon to make a two-holed torus!

    Genus two surface

    (This week we are working on this idea in a geometry session at Cheenta.)


    We want to take a 672 degree polynomial with integer coefficients. Suppose we plugin 673th root of 1 in that polynomial and get 0.

    What can you say about the integer coefficients of this polynomial?

    (This problem will come up in a Complex Number and Geometry session this week.)


    We want to partition the number of shortest paths from (0,0) to (2019, 2019). You are allowed to walk only on the grid (lines with either x coordinate an integer or y coordinate an integer between 0 to 2019)

    Can you take the vertical line x = 673 to partition these set of shortest paths into mutually exclusive and exhaustive subsets of paths?

    (This problem will come up in a Combinatorics session this week.)

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