MathDB

11

Part of 2008 JBMO Shortlist

Problems(2)

2008 JBMO Shortlist G11

Source: 2008 JBMO Shortlist G11

10/10/2017
Consider ABCABC an acute-angled triangle with AB≠ACAB \ne AC. Denote by MM the midpoint of BCBC, by D,ED, E the feet of the altitudes from B,CB, C respectively and let PP be the intersection point of the lines DEDE and BCBC. The perpendicular from MM to ACAC meets the perpendicular from CC to BCBC at point RR. Prove that lines PRPR and AMAM are perpendicular.
JBMOgeometry
greatest n-digit number, 429|n, sum of digits <=11

Source: JBMO 2008 Shortlist N11

10/14/2017
Determine the greatest number with nn digits in the decimal representation which is divisible by 429429 and has the sum of all digits less than or equal to 1111.
JBMOnumber theory