4

Part of 2018 Saudi Arabia GMO TST

Problems(2)

two 2s and two 24s on a 13 x13 board , integers in adjacent cells differ by 1

Source: 2018 Saudi Arabia GMO TST I p4

In each of the cells of a

13 \times 13

board is written an integer such that the integers in adjacent cells differ by

1

. If there are two

2

24

s on this board, how many

13

s can there be?

combinatoricssquare board

max edges in a graph with 8 vertices that contains no cycle of length 4

Source: 2018 Saudi Arabia GMO TST II p4

In a graph with

8

vertices that contains no cycle of length

4

, at most how many edges can there be?

graphedgescombinatoricsgraph theory