Problems(2)
Lotus design
Source: China South East Mathematical Olympiad Grade 10 Prob. 4
7/30/2016
For any four points on a plane, if the areas of four triangles formed are different positive integer and six distances between those four points are also six different positive integers, then the convex closure of points is called a "lotus design."
(1) Construct an example of "lotus design". Also what are areas and distances in your example?
(2) Prove that there are infinitely many "lotus design" which are not similar.
combinatorics
Get back to the camp
Source: 2016 China South East Mathematical Olympiad Grade 11 Problem 4
8/6/2016
A substitute teacher lead a groop of students to go for a trip. The teacher who in charge of the groop of the students told the substitude teacher that there are two students who always lie, and the others always tell the truth. But the substitude teacher don't know who are the two students always lie. They get lost in a forest. Finally the are in a crossroad which has four roads. The substitute teacher knows that their camp is on one road, and the distence is minutes' walk. The students have to go to the camp before it gets dark.
If there are students, and minutes before it gets dark, give a plan that all students can get back to the camp.
If there are students, and minutes before it gets dark, is there a plan that all students can get back to the camp?
combinatoricsChina Southeast MOInteresting problem