Three people at a party discover that the product of any two of their ages is equal to the year in which the third was born.

What is the most recent year the party could have taken place?

Depending on the current year and which calendar system is being used, one or both the age of the party-goers and the year of the party may be different than the given "official" solution.  The year given in the "official" solution is most likely based upon the Gregorian year Current Era (CE)/Anno Domini (AD).
A difference to the "official" solution may then be, for example, the three party-goers are religiously Bahá'í, therefore the date notation used to calculate their birthyears and the year of the party was the Bahá'í Era (BE).

The order given in the list following is by most recent first for the year of the party based upon the date of this post* (which may change over time). Not all calendar systems currently used today are represented here.

                                     Party-goer's
Year of the party              Age  *2008 CE
2550 BE (Buddhist Era)........  50   2551 BE  
1722 AM (Anno Martyrum).......  41   1725 AM  
1122 NS (Nepal Sambat)........  33   1127 NS
  90 ROC(Republic of China)...   9     97 ROC
1406 BS (Bangla Shôn).........  37   1414 BS
 156 BE (Bahá'í Era)..........  12    164 BE
1406 AH (Anno Hegirae)........  37   1492 AH
1980 IE (Incarnation Era).....  44   2001 IE
1980 OS (Old Style)...........  44   2007 OS
1980 AD (Anno Domini).........  44   2008 AD
1892 AJ (Anno Javanico).......  43   1929 AJ
1332 YZ (Yazdegar Sheheriar)..  36   1376 YZ
1332 AP (Anno Persarum).......  36   1386 AP
2652 AS (Anchansakarat).......  51   2698 AS
1122 ME (Malayalam Era).......  33   1183 ME
5700 AM (Anno Mundi)..........  75   5769 AM
1980 BS (Bikram Samwat).......  44   2064 BS
2550 CS (Chulasakarat)........  50   2646 AS
4970 KY (Kaliyuga)............  70   5109 KY

Posted by Dej Mar on 2008-02-21 13:24:02