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Romania Contests
JBMO TST - Romania
2024 Junior Balkan Team Selection Tests - Romania
P5
P5
Part of
2024 Junior Balkan Team Selection Tests - Romania
Problems
(1)
Maximal walk in a special array
Source: Romania JBMO TST 2024 Day 1 P5
7/31/2024
An
n
n
n
-type triangle where
n
⩾
2
n\geqslant 2
n
⩾
2
is formed by the cells of a
(
2
n
+
1
)
×
(
2
n
+
1
)
(2n+1)\times(2n+1)
(
2
n
+
1
)
×
(
2
n
+
1
)
board, situated under both main diagonals. For instance, a
3
3
3
-type triangle looks like this:https://i.ibb.co/k4fmwWY/Screenshot-2024-07-31-153932.pngDetermine the maximal length of a sequence with pairwise distinct cells in an
n
n
n
-type triangle, such that, beggining with the second one, any cell of the sequence has a common side with the previous one.Cristi Săvescu
combinatorics
board