Mr. Ambrose and Mr. Bruford, two senior executives of a London based multinational organisation, embarked on a business tour during the course of the year 2003 A.D. to two of the branches of the organisation located in the capital cities of two different countries. The flag of the country visited by Mr.Ambrose included a blue trapezoid and a green trapezoid as two of its features while the flag of the country corresponding to the city visited by Mr. Bruford contained a purely red circle.

Immediately upon reaching the capital city of the host country, Mr. Ambrose reset his 24 hour wristwatch in accordance with the local time and observed that the date according to his watch was Pth day of the Qth month of 2003, where 2003 when divided separately by P and Q yielded a remainder of 3 in both the cases; both P and Q were greater than 3, and (P+Q) was divisible by 5. Furthermore, it was a FRIDAY according to his watch.

After reaching his hotel room, when it was precisely (x^2) Hours according to his watch, Mr. Ambrose contacted Mr. Bruford for an urgent matter whereby he learnt that the time according to Mr. Bruford's 24 Hour electronic wristwatch (which was also reset in accordance with the local time) at the same instant was exactly ((5/4)*x² +2) hours.

Later during the same day, after returning from an important business meeting to his hotel room, Mr.Ambrose's watch displayed exactly ((5/4)*x²+2) Hours when Mr. Ambrose contacted Mr.Bruford for the second time to discuss the outcome of their respective business meetings; Mr. Bruford's response included the fact that the time by his watch was exactly x Hours.

What cities were visited by Mr. Ambrose and Mr.Bruford? What was the date and time according to their respective wristwatches when Mr. Ambrose contacted Mr. Bruford for the second time?

Note: This problem is based on the global political scenario prevailing in 2003 A.D.

(In reply to re: No Subject by tomarken)

A trapezoid is a quadrilateral (four-sided) geometric figure having two parallel sides.  That the other two sides can not be parallel is not a restriction. Therefore, squares, rectangles, diamonds and other parallelograms are also trapezoids. 

tomarken, I did come up with Djibouti hours ago even just minutes after your initial post, but I wanted to confirm that there was no new flags of that I was unaware, and whether there was a trick with including a date in the problem and its relation with a Daylight Savings Time. 

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I did find that some definitions of a trapezoid do exclude parallelograms, but other definitions do include these quadrilaterals. 

Reference the definition as provided by Wikipedia:

http://en.wikipedia.org/wiki/Trapezoid

It very well may be, and in most probability is, that K Sengupta is one of the authors that chooses to define a Trapezoid as having only one pair of parallel sides.

Edited on March 27, 2006, 1:22 am

Posted by Dej Mar on 2006-03-26 19:33:02