Think #03 23 августа 1997

Puzzle - Born, on fishing, only the square, Well and scissors.

              PUZZLE



             YEAR OF BIRTH



  On a mathematical circle, one of his
Participants - ninth-- offered
mates this puzzle:



        *



             *



                      *



  In recording its all figures are missing. But one
have met three times, marked by asterisks. In the first example 
(multiplication) among the figures both somnozheteley not 
identical. All figures are the product of different, too. In 
the second example (in the division), all 9 digits dividend is 
different and the right of the vertical features of each figure 
is also found only once.


  Determine when the father was born a young mathematician, and 
when he himself, if known, one of the numbers the first 
example, coincides with the birth year of his father and one of 
the numbers second - with the birth year of son.




               Go fishing



  Four avid fisherman - Fadeev, Matveev, Avdeev and Gordeev - 
was caught on 10 fish. Each caught a different number (from 1 to

4) of different fish species: pike, carp, perch,
perch.

  Determine how much fish each of the four species were caught 
Fadeev, Matveev, Avdeev and Gordeev separately, if you know 
that: 

1) the number of pike caught Matveev, as well

   the number of perch caught Gordeev;

2) the number of pike caught Gordeev differ
   is the number of perch caught Av
   Deyev;

3) the number of perch caught Avdeev, equal
   but the number of perch caught Matveev;

4) Gordeev caught four pike;

5) the number of perch caught Matveev, not

   equals the number of carp Fadeeva;

6) Avdeev caught two carp;

7) the number of carp caught Fadeev equilibrium
   but the number of perch caught Avdeev;

8) Fadeev caught a perch.



            Only the square



  Make six-digit number, which has
following properties:

1) the sum of the first two numbers - the square of the number;

2) the sum of the first three numbers - the square of the other
   of numbers;

3) the sum of the last three digits - square

   number;

4) the sum of all six figures - a square number;

5) number written by the first three digits
   square of the number;


6) the number recorded last three digital
   ramie in sequence - square

   number;

7) the number recorded last three digital
   ramie in reverse order - the square of the number
   la;


8) the difference between the square roots of numbers, for
   written word the last three digits, and

   number recorded by the first three digit
   mi - square numbers.



              NU and scissors!



               The figure shows some

            classic scissors and below 8

            (Eight) fantastic.


               As usual izvetsno knife
            boundary cut, when the ends to
            lechkami vault.


               Understand the design

            Eight unusual scissors and times
            divide them into two groups of CO
            lasno principle of action.



      1 2 3 4



          5 6 7 8



             .................