Here are two bona-fide job interview questions, as reported 
by two frazzled interviewees.  They sure could have used some 
help from the Lafayette Problem Group.


[Microsoft]  Your boss wants you to design a calendar that 
she will place on her desk right next to the promotion forms.  
She gives you two plain wooden cubes that will fit 
side-by-side in a wooden holder like so (front view):

                   _____  _____
                _ |     ||     | _
               |X||cube1||cube2||X|
               |X||_____||_____||X|
               |X|--------------|X| 
               |XXXwoodenholderXXX|
                ------------------
 
Your job is to place a single digit between 0 and 9 on each 
of the twelve faces of the cubes so that any day of any month 
can be displayed.  Can you do it?



[D. E. Shaw, a financial firm in NYC]  You and a friend are 
trying to perform the following "magic" trick.  Your friend
leaves the room.  You hand a standard deck of 52 cards to 
someone in the audience.  The audience member chooses any 
five cards from the deck and hands those five cards to you. 
Now, you must select one of these cards to keep concealed 
from your friend, and you must display the other four cards 
side-by-side on a table just like so:

              ___    ___    ___    ___
             |   |  |   |  |   |  |   |
             |   |  |   |  |   |  |   |
             |___|  |___|  |___|  |___|


Your friend now enters the room, examines the only the four 
displayed cards, and then tells the audience what's on the 
concealed card.  (Whoa -- what a neat trick!)

Can you and your friend come up with a scheme so that, based 
solely on the four displayed cards, the fifth card can always 
be determined?