MathDB

4

Part of 2018 May Olympiad

Problems(2)

computational geometry for 15yo, distance inside a parallelogram

Source: May Olympiad (Olimpiada de Mayo) 2018 L2

9/10/2018
In a parallelogram ABCDABCD, let MM be the point on the BCBC side such that MC=2BMMC = 2BM and let NN be the point of side CDCD such that NC=2DNNC = 2DN. If the distance from point BB to the line AMAM is 33, calculate the distance from point NN to the line AMAM.
geometryparallelogramdistance
7 pos. integers with sum 36 around a circle 2018 May Olympiad L1 p4

Source:

8/24/2021
Anna must write 77 positive integers, not necessarily distinct, around a circle such that the following conditions are met: ∙\bullet The sum of the seven numbers equals 3636. ∙\bullet If two numbers are neighbours, the difference between the largest and the smallest is equal to 22 or 33. Find the maximum value of the largest of the numbers that Anna can write.
combinatorics