4

Part of 2018 Bulgaria JBMO TST

Problems(2)

cells of any 2x3 rectangles have different colors

Source: Bulgaria JBMO TST 2018, Day 1, Problem 4

Each cell of an infinite table (infinite in all directions) is colored with one of

n

given colors. All six cells of any

2\times 3

3 \times 2

) rectangle have different colors. Find the smallest possible value of

n

combinatoricsinequalities

672 numbers, what is the minimum of the largest one?

Source: Bulgaria JBMO TST 2018, Day 2, Problem 4

The real numbers

a_1 \leq a_2 \leq \cdots \leq a_{672}

are given such that

a_1 + a_2 + \cdots + a_{672} = 2018.

n \leq 672

n

of these numbers with an integer sum. What is the smallest possible value of

a_{672}