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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
9.3
9.3
Part of
2005 All-Russian Olympiad Regional Round
Problems
(1)
numbers 1-24 on faces 2x2x2 cube All-Russian MO 2005 Regional 9.3
Source:
8/26/2024
Two players take turns placing the numbers
1
,
2
,
3
,
.
.
.
,
24
1, 2, 3,. . . , 24
1
,
2
,
3
,
...
,
24
, in each of the
24
24
24
squares on the surface of a
2
×
2
×
2
2 \times 2 \times 2
2
×
2
×
2
cube (each number can be placed once). The second player wants the sum of the numbers in each cell the rings of
8
8
8
cells encircling the cube were identical. Will he be able to the first player to stop him?
combinatorics