MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2009 All-Russian Olympiad Regional Round
9.4
9.4
Part of
2009 All-Russian Olympiad Regional Round
Problems
(1)
numbers 1-25 into 25 small triangles
Source: All-Russian MO 2009 Regional 9.4
8/27/2024
The picture shows a triangle divided into
25
25
25
smaller triangles, numbered
1
1
1
to
25
25
25
. Is it possible to place the same numbers in the square cells 5
×
5
\times 5
×
5
so that any two numbers written in adjacent triangles were are also written in adjacent cells of the square? (The cells of a square are considered adjacent if they have a common side.) https://cdn.artofproblemsolving.com/attachments/4/3/758fe5531ab3e576ef4712c095b393f8dff397.png
combinatorics