MathDB
1-7 at each box of 7x7 board

Source: XI May Olympiad (Olimpiada de Mayo) 2005 L1 P5

September 22, 2022
combinatorics

Problem Statement

a) In each box of a 7×77\times 7 board one of the numbers is written: 1,2,3,4,5,61, 2, 3, 4, 5, 6 or 77 of so that each number is written in seven different boxes. Is it possible that in no row and no column are consecutive numbers written?
b) In each box of a 5×55\times 5 board one of the numbers is written: 1,2,3,41, 2, 3, 4 or 55 of so that each one is written in five different boxes. Is it possible that in no row and in no column are consecutive numbers written?