1

Part of 1972 Bundeswettbewerb Mathematik

Problems(2)

Minimum sum if lower bound for crosses is given

Source: Bundeswettbewerb Mathematik 1972, round 1, problem 1

There's a real number written on every field of a

n \times n

chess board. The sum of all numbers of a "cross" (union of a line and a column) is

\geq a

. What's the smallest possible sum of all numbers on the board¿

How many fields must a knight walk to...

Source: Bundeswettbewerb Mathematik 1972, round 2, problem 1

Given an infinity chess board and a knight on it. On how many different fields the knight can be after

n

combinatorics proposedcombinatorics