MathDB
Problems
Contests
International Contests
Tournament Of Towns
1994 Tournament Of Towns
(434) 4
(434) 4
Part of
1994 Tournament Of Towns
Problems
(1)
TOT 434 1994 Autumn O S4 numbers in 10x1
Source:
6/12/2024
A rectangular
1
1
1
by
10
10
10
strip is divided into
10
10
10
1
1
1
by
1
1
1
squares. The numbers
1
1
1
,
2
2
2
,
3
3
3
,
.
.
.
...
...
,
10
10
10
are placed in the squares in the following way. First the number
1
1
1
is placed in an arbitrary square, then
2
2
2
is placed in a neighbouring square, then
3
3
3
is placed into a free square neighbouring one of the squares occupied earlier, and so on (up to
10
10
10
). How many different permutations of
1
1
1
,
2
2
2
,
3
3
3
,
.
.
.
...
...
,
10
10
10
can one get in this way? (A Shen)
combinatorics