MathDB

1

Part of ICMC 5

Problems(2)

Integer triangles

Source: ICMC 2022 Round 1 P1

12/4/2021
Let TnT_n be the number of non-congruent triangles with positive area and integer side lengths summing to nn. Prove that T2022=T2019T_{2022}=T_{2019}.
Proposed by Constantinos Papachristoforou
combinatoricscollege contestscountingICMC
integer areas

Source: ICMC 2022 Round 2 P1

3/1/2022
Let SS be a set of 20222022 lines in the plane, no two parallel, no three concurrent. SS divides the plane into finite regions and infinite regions. Is it possible for all the finite regions to have integer area?
Proposed by Tony Wang
geometrycombinatorial geometrycollege contestsICMC