MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
8.5
8.5
Part of
VII Soros Olympiad 2000 - 01
Problems
(1)
1+- brackets , sum 10 (VII Soros Olympiad 2000-01 R1 8.5)
Source:
7/27/2021
Vanya was asked to write on the board an expression equal to
10
10
10
, using only the numbers
1
1
1
, the signs
+
+
+
and
−
-
−
and brackets (you cannot make up the numbers
11
11
11
,
111
111
111
, etc., as well as
(
−
1
)
(-1)
(
−
1
)
). He knows that the bully Anton will then correct all the
+
+
+
signs to
−
-
−
and vice versa. Help Vanya compose the required expression, which will remain equal to
10
10
10
even after Anton's actions.
combinatorics