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Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1988 Flanders Math Olympiad
1988 Flanders Math Olympiad
Part of
Flanders Math Olympiad
Subcontests
(4)
2
1
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3-dimensional cross (quicky)
A 3-dimensional cross is made up of 7 cubes, one central cube and 6 cubes that share a face with it. The cross is inscribed in a circle with radius 1. What's its volume?
4
1
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[solved] - I find this ugly...
Be
R
R
R
a positive real number. If
R
,
1
,
R
+
1
2
R, 1, R+\frac12
R
,
1
,
R
+
2
1
are triangle sides, call
θ
\theta
θ
the angle between
R
R
R
and
R
+
1
2
R+\frac12
R
+
2
1
(in rad). Prove
2
R
θ
2R\theta
2
Rθ
is between
1
1
1
and
π
\pi
π
.
3
1
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good numbers - challenge!
Work base 3. (so each digit is 0,1,2) A good number of size
n
n
n
is a number in which there are no consecutive
1
1
1
's and no consecutive
2
2
2
's. How many good 10-digit numbers are there?
1
1
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polynomial
show that the polynomial
x
4
+
3
x
3
+
6
x
2
+
9
x
+
12
x^4+3x^3+6x^2+9x+12
x
4
+
3
x
3
+
6
x
2
+
9
x
+
12
cannot be written as the product of 2 polynomials of degree 2 with integer coefficients.