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National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2017 Flanders Math Olympiad
3
3
Part of
2017 Flanders Math Olympiad
Problems
(1)
S + V = H + 3 in a closed rectangular neighborhood
Source: Flanders Math Olympiad 2017 p3
12/24/2022
In a closed rectangular neighborhood there are:
S
S
S
streets (these are straight roads of maximum length),
V
V
V
four-arm intersections ( https://cdn.artofproblemsolving.com/attachments/e/4/6a5974a30dc182b59a519a8ef4eb4f1412e05e.png),
H
H
H
city blocks (these are rectangular areas bounded by four streets, which are no be intersected by another street) and
T
T
T
represents the number of
T
T
T
-intersections (https://cdn.artofproblemsolving.com/attachments/0/a/b390a30a0b27d83db681f70f633bdeed697163.png ). For example, in the neighborhood below, there are
15
15
15
streets,
8
8
8
four-arm intersections,
20
20
20
city blocks and
22
22
22
T
T
T
-intersections. https://cdn.artofproblemsolving.com/attachments/a/2/c1a5e463d0fb5671ac0702c91cfc2272d4e2c3.png Prove that in each district
S
+
V
=
H
+
3
S + V = H + 3
S
+
V
=
H
+
3
.
combinatorics