Survo puzzles: www.survo.fi/puzzles
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Problems of April 9, 2007

 

Survo puzzle 51/2007 (35) 

   A  B  C  D  E      
1  5  2  *  *  8  35 
2  *  *  * 11  *  40 
3  *  * 10  *  *  45 
  28 23 24 21 24      



Survo puzzle 52/2007 (530) 

   A  B  C  D  E      
1  *  * 17  3  *  49 
2  *  *  *  * 11  60 
3  5 18  *  *  *  46 
4  *  7 12  *  *  55 
  42 41 41 42 44      



Survo puzzle 53/2007 (1100 without the hint) 

   A  B  C  D      
1  *  *  *  *  27 
2  *  *  *  *  13 
3  *  *  *  *  53 
4  *  *  *  *  43 
  47 39 29 21      

Hint: Let X be the positive root of the quadratic equation
456*X^2+1416*X-131=0. Then X can be represented as a continued fraction

          1
X = -----------------
              1
    A1 + -----------------
                  1
         B1 + ------------
                      1
              C1 + -------
                   D1 + X

and this gives the the first row of the table.

In Survo these numbers can be evaluated, for example, by the following
recursive formulas of editorial computing:

Y(N,X):=if(N=0)then(X)else(1/(Y(N-1,X)-A(N-1,X)))
A(N,X):=if(N=0)then(int(X))else(int(Y(N,X)))



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