<html> <body dir="rtl"> <p align="right"> 1.  <img src="senior1.gif">  <img src="senior2.gif">  <img src="senior3.gif">     . <br>  m -n  ,      m<n.  <img src="senior4.gif">.    2      ,  <img src="senior5.gif">   - <img src="senior6.gif">  (a=n-m>0)   : <img src="senior7.gif">  <img src="senior8.gif">  <img src="senior9.gif"> (        2  2    2 -4).    : <img src="senior10.gif"> </p> <hr> <p> 2.    ,    .<br>    ,    .<br> ,       r -R    b.  r+b=B       R(r+b)=RB  .    R(r+b)=Rr+Rb=b+Rb        ,   .  ,        .<br> ***<br>             :<br>           (        ).  <b>R</b>    .   1,     .   r   .   -<b>R</b>  : r=n<b>R</b>+c.  c   0,    (   -<b>R</b>) -n<b>R</b>  ,   r   .      -<b>R</b>    -<b>R</b> .     .            .<br> </p> <hr> <p> 3. <br> <img src="senior11.gif"> <br><br> <img src="senior12.gif"> <br>  -9-  3.4      -100. </p> <hr> <p> 4.       :<br> 3 : '     1,2 <br> 4 : '      1,3  '  <br> 5 : '     1,4     4     .<br> 6 : '     2,4   4    ,  '  <br> 7 :  '     1,6  2,5,   (   5 -6    ).       3,4.   3    (1,2)   4  2  (1,3 -> 1, 1, 2), " 3   '  ' .<br> 8 : '    1,7  (   7     )<br> 9 : '    7,2 <br> 10 : '    1,9  2,8,   (   8 -9    ),     3,7,    3     7   ,  " '   ,      4,6,    4      6   ,  '    . " '   .<br> 11 : '    1,10  (   10    )<br> 13 : '     5,8.      ':<br> 5->1,4:   4      8   ,    ' .<br> 5->2,3: '       8 -3,5.  '     3, '       3   ,   5   ,  '.<br> 8->1,7: '   5->1,4;   4        7   ,  '<br> 8->2,6: '   6->1,5.   2   5     ', '            .<br> 8->3,5: '     5 -2,3;  '     3, '       3   ,   5   ,  '.<br>   '     13 . <br> <br>    ,  ,   (  )      N  N=30 !!!     ' ( )   . <br>    N-  : 1, 2, 4, 7, 10, 20, 23, 26.                . <a target="_top" href= "http://www.research.att.com/~njas/sequences/?q=1%2C2%2C4%2C+7%2C+10%2C+20%2C+23%2C+26&language=english">         '  1000 </a>,     ,   Grundy's game        .    '     . </p> <hr> <p> 5. <a href= "OR6_5.doc">      -WORD  4  . </a> <br> <font COLOR=#e03010>   ( )    5/3/2006    ' ,   ' . <font COLOR=#0> </p> </body> </html>