MathDB
Problems
Contests
National and Regional Contests
Peru Contests
Peru Cono Sur TST
2015 Peru Cono Sur TST
P1
P1
Part of
2015 Peru Cono Sur TST
Problems
(1)
High score with dominoes
Source: 2015 Peru Cono Sur TST P1
7/10/2023
A
A
A
writes, at his choice,
8
8
8
ones and
8
8
8
twos on a
4
×
4
4\times 4
4
×
4
board. Then
B
B
B
covers the board with
8
8
8
dominoes and for each domino she finds the smaller of the two numbers that that domino covers. Finally,
A
A
A
adds these
8
8
8
numbers and the result is her score. What is the highest score
A
A
A
can secure, no matter how
B
B
B
plays? Clarification: A domino is a
1
×
2
1\times 2
1
×
2
or
2
×
1
2\times 1
2
×
1
rectangle that covers exactly two squares on the board.
combinatorics