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18
Math Prize 2019 Problem 18
Math Prize 2019 Problem 18
Source:
October 15, 2019
Math Prize for Girls
Problem Statement
How many ordered triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of integers with
−
15
≤
a
,
b
,
c
≤
15
-15 \le a, b, c \le 15
−
15
≤
a
,
b
,
c
≤
15
are there such that the three equations
a
x
+
b
y
=
c
ax + by = c
a
x
+
b
y
=
c
,
b
x
+
c
y
=
a
bx + cy = a
b
x
+
cy
=
a
, and
c
x
+
a
y
=
b
cx + ay = b
c
x
+
a
y
=
b
correspond to lines that are distinct and concurrent?
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