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National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
1991 Greece Junior Math Olympiad
1991 Greece Junior Math Olympiad
Part of
Greece Junior Math Olympiad
Subcontests
(4)
4
1
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x^4+y^4 in terms of x+y=a, xy=b - Greece Juniors 1991 p4
Let
x
+
y
=
a
x+y=a
x
+
y
=
a
and
x
y
=
b
xy=b
x
y
=
b
. Calculate exression
x
4
+
y
4
x^4+y^4
x
4
+
y
4
in terms of
a
a
a
and
b
b
b
.
3
1
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sum of 4 -digit numbers from 2-6 - Greece Juniors 1991 p3
Find the sum of all
4
4
4
-digit numbers using the digits
2
,
3
,
4
,
5
,
6
2,3,4,5,6
2
,
3
,
4
,
5
,
6
without a repetition of any of those digits.
2
1
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area of semicircle - Greece Juniors 1991 p2
Given a semicircle of diameter
A
B
AB
A
B
and center
O
O
O
. Let
C
D
CD
C
D
be the chord of the semicircle tangent to two circles of diameters
A
O
AO
A
O
and
O
B
OB
OB
. If
C
D
=
120
CD=120
C
D
=
120
cm,, caclulate area of the semicircle.
1
1
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430 apples for 30 kids - Greece Juniors 1991 p1
In a class of
30
30
30
kids are distributed
430
430
430
apples . Prove that at least two kids will take the same number of apples.