4
Problems(2)
Combinatorics+Number Theory and a bord to solve
Source: 2023 Girls in Mathematical Tournament- Level A, Problem 4
10/29/2023
Determine all positive integers such that exists an where we can write times each of the numbers from to (one number in each cell), such that the sums of numbers in each line leave distinct remainders in the division by , and the sums of numbers in each column leave distinct remainders in the division by .
combinatoricsnumber theory
Can you construct the incenter of a triangle ABC?
Source: 2023 Girls in Mathematics Tournament- Level B, Problem 4
10/29/2023
Given points and , Jaqueline has a ruler that allows tracing the line . Jaqueline also has a special object that allows the construction of a circle of diameter . Also, always when two circles (or a circle and a line, or two lines) intersect, she can mark the points of the intersection with a pencil and trace more lines and circles using these dispositives by the points marked. Initially, she has an acute scalene triangle . Show that Jaqueline can construct the incenter of .
geometryincenter