4

Part of 1995 All-Russian Olympiad

Problems(2)

numbers from 1 to 81 be written in a $9×9$ board

Source: All-Russian olympiad 1995, Grade 9, First Day, Problem 4

Can the numbers from 1 to 81 be written in a 9×9 board, so that the sum of numbers in each 3×3 square is the same? S. Tokarev

combinatorics proposedcombinatorics

all angles of a convex $n$-gon are equal

Source: All-Russian olympiad 1995, Grade 10, First Day, Problem 4

Prove that if all angles of a convex

n

-gon are equal, then there are at least two of its sides that are not longer than their adjacent sides. A. Berzin’sh, O. Musin

geometry proposedgeometry