2016 JBMO Problems
Problem 1
A trapezoid (,) is circumscribed.The incircle of the triangle touches the lines and at the points and ,respectively.Prove that the incenter of the trapezoid lies on the line .
Problem 2
Let be positive real numbers.Prove that
.
Problem 3
Find all triplets of integers such that the number
is a power of .
(A power of is an integer of form ,where is a non-negative integer.)
Problem 4
A table is called regular f each of its cells contains one of four pairwise distinct real numbers,such that each of them occurs exactly one in every subtable.The sum of all numbers of a regular table is called the total sum of the table.With any four numbers,one constructs all possible regular tables,computes their total sums and counts the distinct outcomes.Determine the maximum possible count.
See also
2016 JBMO (Problems • Resources) | ||
Preceded by 2015 JBMO Problems |
Followed by 2017 JBMO Problems | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |