MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Girls in Math at Yale
2021 Girls in Math at Yale
R1
R1
Part of
2021 Girls in Math at Yale
Problems
(1)
GiM at Yale 2021 Mathathon R1: sillyalg/hextriangles/sirenaprimes
Source:
2/28/2021
1. If
5
x
+
3
y
−
z
=
4
5x+3y-z=4
5
x
+
3
y
−
z
=
4
,
x
=
y
x=y
x
=
y
, and
z
=
4
z=4
z
=
4
, find
x
+
y
+
z
x+y+z
x
+
y
+
z
.2. How many ways are there to pick three distinct vertices of a regular hexagon such that the triangle with those three points as its vertices shares exactly one side with the hexagon?3. Sirena picks five distinct positive primes,
p
1
<
p
2
<
p
3
<
p
4
<
p
5
p_1 < p_2 < p_3 < p_4 < p_5
p
1
<
p
2
<
p
3
<
p
4
<
p
5
, and finds that they sum to
192
192
192
. If the product
p
1
p
2
p
3
p
4
p
5
p_1p_2p_3p_4p_5
p
1
p
2
p
3
p
4
p
5
is as large as possible, what is
p
1
−
p
2
+
p
3
−
p
4
+
p
5
p_1 - p_2 + p_3 - p_4 + p_5
p
1
−
p
2
+
p
3
−
p
4
+
p
5
?
Yale
college