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    1: <problem>
    2: <script type="loncapa/perl"># Construct an Egyptian Fraction that can be represented by three terms with denominators between 3 and 12
    3: @denominators=(&random_permutation(&random(1,1000,1),(3..12)))[0..2];
    4: $egyptian='1/'.(join('+1/',sort{$a<=>$b}(@denominators)));
    5: $possible="A possible solution is $egyptian";
    6: 
    7: # Let the CAS figure out the value
    8: $solution=&cas('maxima',$egyptian);
    9: 
   10: # Subroutine that checks if the provided term is indeed an Egyptian Fraction
   11: sub analyze {
   12:     my ($expression)=@_;
   13:     $expression=~s/\s//gs;
   14:     $expression=~s/\+?1\//\,/gs;
   15:      if ($expression=~/^(\,[0-9]+)+$/) {
   16: # Format is indeed 1/n+1/m+...
   17:         $last=-1;
   18:         foreach $number (sort { $a<=>$b } split(/\,/,$expression)) {
   19: # Is a number used twice?
   20:              if ($last==$number) { return(0,1); }
   21:              $last=$number;
   22:           }
   23:           return(0,0);
   24:      }
   25:      return(1,0);
   26: }
   27: </script>
   28: 
   29: <startouttext />
   30: 
   31: Write $solution as an Egyptian Fraction<br />
   32: <endouttext />
   33: 
   34: <customresponse answerdisplay="$possible" id="11">
   35:     <answer type="loncapa/perl"># Analyze the format
   36: ($formaterror,$doubleerror)=&analyze($submission);
   37: if ($formaterror || $doubleerror) { return 'BAD_FORMULA'; }
   38: # It is an Egyptian Fraction, is the value correct?
   39: if (&cas('maxima',$submission.'-('.$egyptian.')') eq '0') {
   40:     return 'EXACT_ANS';
   41: }
   42: return 'INCORRECT';</answer>
   43:     <textline readonly="no" size="40" />
   44: 
   45:  <customhint name="format" id="12">
   46:       <answer type="loncapa/perl">if ((&analyze($submission))[0]) { return 'EXACT_ANS'; }
   47: return 'INCORRECT';</answer>
   48: </customhint>
   49: <hintpart on="format">
   50: <startouttext />
   51: <p>
   52: Egyptian Fractions have a format of 1/number+1/number+..., for example 1/3+1/17+1/52. 
   53: </p>
   54: <endouttext />
   55: </hintpart>
   56:  <customhint name="double" id="13">
   57:       <answer type="loncapa/perl">if ((&analyze($submission))[1]) { return 'EXACT_ANS'; }
   58: return 'INCORRECT';</answer>
   59: </customhint>
   60: <hintpart on="double">
   61: <startouttext />
   62: <p>
   63: Egyptian Fractions cannot have the same denominator more than once. For example, 1/3+1/17+1/4+1/17 is not an Egyptian Fraction, as it has 17 twice as denominator.
   64: </p>
   65: <endouttext />
   66: </hintpart>
   67: </customresponse>
   68: </problem>
   69: