MathDB

7

Part of 2008 Hanoi Open Mathematics Competitions

Problems(2)

<DAC+<EBD+<ACE+<BDA+<CEB in covex pentagon (2008 HOMC Junior Q7)

Source:

7/18/2019
The figure ABCDEABCDE is a convex pentagon. Find the sum ∠DAC+∠EBD+∠ACE+∠BDA+∠CEB\angle DAC + \angle EBD +\angle ACE +\angle BDA + \angle CEB?
geometryconvexpentagonangles
a,b,c consecutive odd, a^2+b^2+c^2 = 4 equal digits (HOMC 2008 Q7)

Source:

7/25/2019
Find all triples (a,b,c)(a, b,c) of consecutive odd positive integers such that a<b<ca < b < c and a2+b2+c2a^2 + b^2 + c^2 is a four digit number with all digits equal.
number theoryDigits