9. The desks in the TAIMC contest r

9. The desks in the TAIMC contest room are arranged in a 6 × 6 configuration.
Two contestants are neighbours if they occupy adjacent seats along a row, a
column or a diagonal. Thus a contestant in a seat at a corner of the room has 3
neighbours, a contestant in a seat on an edge of the room has 5 neighbours, and a
contestant in a seat in the interior of the room has 8 neighbours. After the contest,
a contestant gets a prize if at most one neighbour has a score greater than or
equal to the score of the contestant. What is maximum number of prize-winners?
【Solution】
Divide the contest room into 9 sections each of which is a 2 × 2 configuration. In
each section, arrange the four contestants in order of their scores starting with the
highest. Then the contestant third or fourth in the line cannot be prize-winners
because each would have at least two neighbours whose scores are not lower. Hence
the maximum number of prize-winners is 2 × 9 = 18. The diagram below shows the
marks of the contestants in the respective seats, and each contestant in the first, third
or fifth row get a prize.

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10 10 10 10 10 10
40 50 60 70 80 90
10 10 10 10 10 10
40 50 60 70 80 90
10 10 10 10 10 10
ANS: 18

ผลลัพธ์ (อังกฤษ) 1:

9th. the desks in the taimc contest room are arranged in a 6 × 6 configuration.
Two contestants are neighbours if they occupy adjacent seats along a row, a
column or a diagonal. thus a contestant in a seat at a corner of the room has 3
neighbours, a contestant in a seat on an edge of the room has 5 neighbours, and a
contestant in a seat in the interior of the room has 8 neighbours.after the contest,
a contestant gets a prize if at most one neighbour has a score greater than or
equal to the score of the contestant. what is maximum number of prize-winners? 】 【Solution

divide the contest room into 9 sections each of which is a 2 × 2 configuration. in
each section, arrange the four contestants in order of their scores starting with the
highest.then the contestant third or fourth in the line cannot be prize-winners
because each would have at least two neighbours whose scores are not lower. hence
the maximum number of prize-winners is 2 × 9 = 18. the diagram below shows the
marks of the contestants in the respective seats, and each contestant in the first, third
or fifth row get a prize.


40 50 60 70 80 90 10 10 10 10 10 10
.40 50 60 70 80 90
10 10 10 10 10 10
40 50 60 70 80 90
10 10 10 10 10 10
ans: 18.

ผลลัพธ์ (อังกฤษ) 3:

9.The TAIMC desks in the contest room are arranged in a configuration 6 × 6.
Two neighbours contestants are adjacent if they occupy seats along a row, a column or a diagonal
. Thus a contestant in a seat at a corner of the room has 3
neighbours, a contestant in a seat on an edge of the room has 5 neighbours,
and a contestant in a seat in the interior of the room has 8 neighbours.The After contest,
a contestant gets a prize if at most one neighbour
has a score greater than or equal to the score of the contestant.What is maximum number of prize-winners?

【 Solution 】 Divide contest the room into 9 sections each of which is a 2 × 2 configuration. In
each section, arrange the four contestants in order of their scores starting with the highest
.The Then contestant in the third or fourth line cannot be prize-winners
because each would have at least two neighbours whose scores are not lower.Hence
the maximum number of prize-winners is 2× 9 =18.
The diagram below shows the marks of the contestants in the respective seats, and each contestant in the first, third or fifth row
get a prize.


40 50 60 70 80 90 10 10 10 10 10 10
40 50 60 70 80 90 10 10 10 10 10 10


40 50 60 70 80 90 10 10 10 10 10 10
ANS: 18