<PRE><B>Question 1102983</B>
10Cr=20C(r+1)
==============================

This is an old one… and has no solution.

{{{ 10Cr  &lt;&gt; 20C(r+1) }}}  for all values of r.  

There are only 11 values to check (after the first 6 it is pretty obvious 
they can never be equal, but all 11 values are listed for completeness):

{{{ 10C0 = 1  &lt;&gt; 20C1 = 20 }}}
{{{ 10C1 = 10 &lt;&gt; 20C2 = 190 }}}
{{{ 10C2 = 45 &lt;&gt; 20C3 = 1140 }}}
{{{ 10C3 = 120 &lt;&gt; 20C4 = 4845 }}}
{{{ 10C4 = 210 &lt;&gt; 20C5 = 15504 }}}
{{{ 10C5 = 252 &lt;&gt; 20C6 = 38760 }}}
{{{ 10C6 = 210 &lt;&gt; 20C7 = 77520 }}} 
{{{ 10C7 = 120 &lt;&gt; 20C8 = 125970 }}} 
{{{ 10C8 = 45 &lt;&gt; 20C9 = 167960 }}} 
{{{ 10C9 = 10 &lt;&gt; 20C10 = 184756 }}} 
{{{ 10C10 = 1 &lt;&gt; 20C11 = 167960 }}} 
</PRE>