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(3): 24 hour time? (part spoiler) by Vernon Lewis)

I still don't agree that an adjustment is necessary.  When Mr Ambrose arrives in city A, he sets his watch according to city A's local time.  At the same instant in city B, Mr Bruford sets his watch according to city B's local time.  That is why their watches show two different times when they compare.  There shouldn't be any need to adjust the equations.

Maybe I am interpreting the 24-hour time thing wrong and I was making it too complicated.  What if x=4, as in 4 o'clock?  That would lead to the following solution:

Mr Ambrose arrives in city A at 16 o'clock (x^2, or 4 pm).  At the same time, Mr Bruford arrives in city B, where it is 22 o'clock ((5/4)*x² +2, or 10 pm).  There is a 6 hour time difference, obviously. 

They both leave for meetings and arrive back six hours later.  At that point, it is 22 o'clock ((5/4)*x² +2, or 10 pm) in city A, and 4 o'clock (x, or 4 am) in city B.

Mr Bruford would be in Tokyo, Japan (GMT +9) and Mr Ambrose would be in Djibouti, Djibouti (GMT +3).  When they contact each other the second time, Mr Ambrose's watch displays 2200 hours (10 pm) on October 10, 2003.  Mr Bruford's watch displays 400 hours (4 am) on October 11, 2003.

Posted by tomarken on 2006-03-26 14:03:12