MathDB

2

Part of 2015 Tuymaada Olympiad

Problems(2)

Perpendicular angle bisectors

Source: Tuymaada 2015, Day 1, Problem 2, Senior League

7/10/2017
DD is midpoint of ACAC for △ABC\triangle ABC. Bisectors of ∠ACB,∠ABD\angle ACB,\angle ABD are perpendicular. Find max value for ∠BAC\angle BAC
(S. Berlov)
geometryangle bisector
Funny numbers

Source: Tuymaada 2015, Day 1, Problem 2, Junior League

7/10/2017
We call number as funny if it divisible by sum its digits +1+1.(for example 1+2+1∣12 1+2+1|12 ,so 1212 is funny) What is maximum number of consecutive funny numbers ?
O. Podlipski
number theory