MathDB

3

Part of ICMC 5

Problems(2)

Determinants equal mod 2

Source: ICMC 2022 Round 1 P3

12/4/2021
Let M\mathcal M be the set of n×nn\times n matrices with integer entries. Find all A∈MA\in\mathcal M such that det⁡(A+B)+det⁡(B)\det(A+B)+\det(B) is even for all B∈MB\in\mathcal M.
Proposed by Ethan Tan
linear algebracollege contestsDeterminantsICMC
Every affine projection has point symmetry

Source: ICMC 2022 Round 2 P3

3/1/2022
A set of points has point symmetry if a reflection in some point maps the set to itself. Let P\cal P be a solid convex polyhedron whose orthogonal projections onto any plane have point symmetry. Prove that P\cal P has point symmetry.
Proposed by Ethan Tan
ICMCgeometrycombinatorial geometry3D geometrycollege contestssymmetry