Showing posts with label contradiction. Show all posts
Showing posts with label contradiction. Show all posts

Thursday, April 16, 2015

Olympiad Trigonometric Problem (Continued)

 Previously we asked you, the educators or yourself, if you are a student to think of way(s) to find the ratio of $\dfrac{PR}{QR}$ in this thread (Olympiad Trigonometric Problem), we will now lead you to a credible way to solve for that intriguing hard trigonometric problem.

We in fact, should have the eagle eye sight and should be able to tell offhand that we suspect $\angle P=\angle Q$. 

Wednesday, April 15, 2015

When is Cheryl's birthday?

Question ((Singapore and Asian Schools Math Olympiad test 2015))

Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
May 15             May 16         May 19
June 17             June 18                     
July 14              July 16                      
August 14       August 15      August 17    

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

   Albert:  I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
Bernard:  At first I don't know when Cheryl's birthday is, but I know now.                                 
   Albert:  Then I also know when Cheryl's birthday is.                                                           

So, when is Cheryl's birthday?