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Guest Message by DevFuse
 

BMAD

Member Since 18 Feb 2013
Offline Last Active Nov 26 2014 02:26 PM
*****

Topics I've Started

6 Squares and a Common Point

21 November 2014 - 02:43 PM

As a follow up to my circles problem:

 

Given six squares where any group of five have two common points.  Does there exist a common point for all 6?


Chess Tournament

18 November 2014 - 12:23 AM

Eight men had participated in the chess tournament. (Each meets each; draws are allowed, giving 1/2 of a point; winner gets 1.) Everyone has a different number of points. The second one has as many points as the four weakest participants together. 

 

What was the result of the play between the third prizer and the chess-player that have occupied the seventh place?

 

 

Five circles and common points

18 November 2014 - 12:21 AM

Given five circles where any group of 4 have a common point.  Does there exist a common point for all 5?


maximal triangle area

18 November 2014 - 12:19 AM

What is the maximal area of a triangle if its sides a,b,c satisfying the inequality: 0<=a<=1<=b<=2<=c<=3?


The 1962-digit number

18 November 2014 - 12:17 AM

Given 1962 -digit number that is divisible by 9. Let x be the sum of its digits. Let the sum of the digits of x be y. Let the sum of the digits of y be z. 

Find z.