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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2023 Junior Balkan Team Selection Tests - Moldova
4
4
Part of
2023 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
(a, 2ad+b, ad^2+bd+c)
Source: Moldova JTST 2023
5/5/2023
On the board there are three real numbers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
. During a
p
r
o
c
e
d
u
r
e
procedure
p
roce
d
u
re
the numbers are erased and in their place another three numbers a written, either
(
c
,
b
,
a
)
(c,b,a)
(
c
,
b
,
a
)
or every time a nonzero real number
d
d
d
is chosen and the numbers
(
a
,
2
a
d
+
b
,
a
d
2
+
b
d
+
c
)
(a, 2ad+b, ad^2+bd+c)
(
a
,
2
a
d
+
b
,
a
d
2
+
b
d
+
c
)
are written. 1) If we start with
(
1
,
−
2
,
−
1
)
(1,-2,-1)
(
1
,
−
2
,
−
1
)
written on the board, can we have the numbers
(
2
,
0
,
−
1
)
(2,0,-1)
(
2
,
0
,
−
1
)
on the board after a finite number of procedures? 2) If we start with
(
1
,
−
2
,
−
1
)
(1,-2,-1)
(
1
,
−
2
,
−
1
)
written on the board, can we have the numbers
(
2
,
−
1
,
−
1
)
(2,-1,-1)
(
2
,
−
1
,
−
1
)
on the board after a finite number of procedures?
combinatorics