MathDB

2011 May Olympiad

Part of May Olympiad

Subcontests

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Some points in a circle with 0 and 1 write on them

Given nn points in a circle, Arnaldo write 0 or 1 in all the points. Bernado can do a operation, he can chosse some point and change its number and the numbers of the points on the right and left side of it. Arnaldo wins if Bernado can´t change all the numbers in the circle to 0, and Bernado wins if he can
a) Show that Bernado can win if n=101n=101 b) Show that Arnaldo wins if n=102n=102

no of cubes to assemble large cube May Olympiad (Olimpiada de Mayo) 2011 L1 P4

Using several white edge cubes of side 1 1, Guille builds a large cube. Then he chooses 44 faces of the big cube and paints them red. Finally, he takes apart the large cube and observe that the cubes with at least a face painted red is 431431. Find the number of cubes that he used to assemble the large cube. Analyze all the possibilities.
3
2

starting with a right triangle, angles between two lines wanted

In a right triangle rectangle ABCABC such that AB=ACAB = AC, MM is the midpoint of BCBC. Let PP be a point on the perpendicular bisector of ACAC, lying in the semi-plane determined by BCBC that does not contain AA. Lines CPCP and AMAM intersect at QQ. Calculate the angles that form the lines APAP and BQBQ.

area inside a rectangle (May Olympiad 2011 L1)

In the rectangle ABCD,BC=5,EC=1/3CDABCD, BC = 5, EC = 1/3 CD and FF is the point where AEAE and BDBD are cut. The triangle DFEDFE has area 1212 and the triangle ABFABF has area 2727. Find the area of the quadrilateral BCEFBCEF . https://1.bp.blogspot.com/-4w6e729AF9o/XNY9hqHaBaI/AAAAAAAAKL0/eCaNnWmgc7Yj9uV4z29JAvTcWCe21NIMgCK4BGAYYCw/s400/may%2B2011%2Bl1.png