
Tough Puzzles
The Contest Center 59 DeGarmo Hills Road Wappingers Falls, NY 12590 

The Johnsons, the Jensens and the Jansons all hold a big party. Everyone shakes hands with every member of the other two families, 142 handshakes in all. Assuming that there at least as many Jensens as Johnsons, and at least as many Jansons as Jensens, how many of each family are present? 
1  This is a numbered list of twelve statements.  
2  Exactly 3 of the last 6 statements are true.  
3  Exactly 2 of the evennumbered statements are true.  
4  If statement 5 is true, then statements 6 and 7 are both true.  
5  The 3 preceding statements are all false.  
6  Exactly 4 of the oddnumbered statements are true.  
7  Either statement 2 or 3 is true, but not both.  
8  If statement 7 is true, then 5 and 6 are both true.  
9  Exactly 3 of the first 6 statements are true.  
10  The next two statements are both true.  
11  Exactly 1 of statements 7, 8 and 9 are true.  
12  Exactly 4 of the preceding statements are true. 
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