3

Part of ICMC 2

Problems(2)

ICMC 2018/19 Round 1, Problem 3

Source: Imperial College Mathematics Competition 2018/19 - Round 1

A ‘magic square’ of size

n

n\times n

array of real numbers such that all the rows, all the columns and the two main diagonals have the same sum. Determine the dimension, over

\mathbb{R}

, of the vector space of

n\times n

magic squares.\\

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ICMC 2018/19 Round 2, Problem 3

Source: Imperial College Mathematics Competition 2018/19 - Round 2

Show that if the faces of a tetrahedron have the same area, then they are congruent.

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