MathDB

2

Part of 2009 JBMO Shortlist

Problems(4)

Mathenatics

Source: JBMO 2009 Shortlist

5/3/2016
A2\boxed{A2} Find the maximum value of z+xz+x if x,y,zx,y,z are satisfying the given conditions.x2+y2=4x^2+y^2=4 z2+t2=9z^2+t^2=9 xt+yz≥6xt+yz\geq 6
algebra
5 players, 2 players vs 2 players in a tournament

Source: JBMO 2009 Shortlist C2

10/14/2017
Five players (A,B,C,D,E)(A,B,C,D,E) take part in a bridge tournament. Every two players must play (as partners) against every other two players. Any two given players can be partners not more than once per a day. What is the least number of days needed for this tournament?
JBMOcombinatoricsexamples
2009 JBMO Shortlist G2

Source: 2009 JBMO Shortlist G2

10/8/2017
In right trapezoid ABCD(AB∥CD){ABCD \left(AB\parallel CD\right)} the angle at vertex BB measures 75∘{{75}^{{}^\circ }}. Point H{H}is the foot of the perpendicular from point A{A} to the line BC{BC}. If BH=DC{BH=DC} andAD+AH=8{AD+AH=8}, find the area of ABCD{ABCD}.
geometryJBMO
pirates with total 2009 coins, each 1 more than the younger

Source: JBMO 2009 Shortlist N2

10/14/2017
A group of n>1n > 1 pirates of different age owned total of 20092009 coins. Initially each pirate (except the youngest one) had one coin more than the next younger. a) Find all possible values of nn. b) Every day a pirate was chosen. The chosen pirate gave a coin to each of the other pirates. If n=7n = 7, find the largest possible number of coins a pirate can have after several days.
JBMOnumber theory