MathDB

1

Part of 2000 France Team Selection Test

Problems(2)

France TST 2000 D1Q1

Source:

3/2/2013
Points P,Q,R,SP,Q,R,S lie on a circle and ∠PSR\angle PSR is right. H,KH,K are the projections of QQ on lines PR,PSPR,PS. Prove that HKHK bisects segment QS QS.
geometryrectanglecircumcirclegeometry unsolved
France TST 2000 D2Q1

Source:

3/2/2013
Some squares of a 1999×19991999\times 1999 board are occupied with pawns. Find the smallest number of pawns for which it is possible that for each empty square, the total number of pawns in the row or column of that square is at least 19991999.
combinatorics unsolvedcombinatorics