From: bultman@dgw.rws.nl (G.W.Bultman)
Newsgroups: rec.puzzles
Subject: 26-62 Solution (LaTeX)
Date: 13 Oct 1992 07:23:31 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu


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\documentstyle[dina4,amstex]{article}
\pagestyle{\empty}
\begin{document}

\newcommand\three{\frac{6}{2}}
\newcommand\twentyseven{ {(\three)}^{(\three)} }

\noindent{\bf Puzzle (continued)}: 

\noindent Make the numbers 26-62 using only 2's and 6's and the operators
$+$,$-$,$\times$,$/$,$!$,$\sqrt{\phantom{0}}$ and $**$ (exponentiation).
An extra conditon is that for each number an {\bf equal} number of 2's and 
6's must be used ({\tiny Original puzzle by G.W.Bultman}).

\bigskip

\noindent{\bf Remarks}:

\noindent In choosing the `best' solutions, the solution with the least
number of digits always `won'; when tied, the solution using the least 
number of operators was preferred; in case of another tie, the solution 
with the least complex operators was chosen. 
Required brackets were counted as one operator:
$(\frac{6}{2})!$ has 3 operators (couting the brackets), 
$ (6-2)+\frac{6}{2} $ also has 3 operators.

\noindent The solutions for 
41 ($26+\binom{6}{2}$),
47 ($62-\binom{6}{2}$),
49 ($2^6+\binom{6}{2}$) and 51 ($6^2+\binom{6}{2}$) by JvdL using the 
binomial operator are noted, but discarded.

\bigskip

\noindent{\bf Contributors}:

\begin{list}{$\bullet$}{\itemsep 0in \parsep 0in}
\item Hans Braker, $<$witajgb\@dutinfh.tudelft.nl$>$
\item Janneke v.d. Linden, $<$linden\@dgw.rws.nl$>$
\item Michael Maciolek, $<$mikem\@ll.mit.edu$>$
\item T. Steidten, $<$Steidten\@mathematik.tu-chemnitz.de$>$
\item Gert Bultman, $<$bultman\@dgw.rws.nl$>$
\end{list}

\newpage

\noindent{\bf Solution}:

% make the strut 3pt taller and 3pt deeper than the entry for 27
\setbox0=\hbox{${(\frac{6}{2})}^{(\frac{6}{2})}$}%
\dimen0=\ht0 \advance\dimen0 by 3pt
\dimen2=\dp0 \advance\dimen2 by 3pt
\setbox\strutbox\hbox{\vrule width0pt depth\dimen2 height \dimen0 }

\begin{center}
\begin{tabular}{|rc|rc|}
\multicolumn{1}{c}{\rule{1.5cm}{0pt}}&
\multicolumn{1}{c}{\rule{5cm}{0pt}}&
\multicolumn{1}{c}{\rule{1.5cm}{0pt}}&
\multicolumn{1}{c}{\rule{5cm}{0pt}} \\ [-25pt]
\multicolumn{4}{c}{\bf \LARGE 26-62 } \\ \hline
26: & $ 26                        $ & 45: & $ \frac{6!}{(6-2)^2}     $ \\ \hline
27: & $ \twentyseven              $ & 46: & $ 2\times26-6            $ \\ \hline
28: & $ 2^6-6^2                   $ & 47: & $ 66-22+\three           $ \\ \hline
29: & $ 26+\three                 $ & 48: & $ 6^2+2\times6           $ \\ \hline
30: & $ 26+6-2                    $ & 49: & $ \frac{222}{6}+6+6      $ \\ \hline
31: & $ \frac{66}{2}-2            $ & 50: & $ 62-6\times2            $ \\ \hline
32: & $ 6\times6-2\times2         $ & 51: & $ 62-6-\three-2          $ \\ \hline
33: & $ 6^2-\three                $ & 52: & $ 26+26                  $ \\ \hline
34: & $ 22+6+6                    $ & 53: & $ 26+\twentyseven        $ \\ \hline
35: & $ 6\times6-\frac{2}{2}      $ & 54: & $ 62-6-2                 $ \\ \hline
36: & $ 6^2                       $ & 55: & $ 2\times22+\frac{66}{6} $ \\ \hline
37: & $ 6\times6+\frac{2}{2}      $ & 56: & $ 2^6-6-2                $ \\ \hline
38: & $ 26+2\times6               $ & 57: & $ 62-6+\three-2          $ \\ \hline
39: & $ \frac{62}{2}+6            $ & 58: & $ 6\times6+22            $ \\ \hline
40: & $ 6\times6+2\times2         $ & 59: & $ 62-\three              $ \\ \hline
41: & $ 66-22-\frac{6}{2}         $ & 60: & $ 2^6-6+2                $ \\ \hline
42: & $ (6+\frac{2}{2})\times6    $ & 61: & $ 2^6-\three             $ \\ \hline
43: & $ 2\times26-6-\three        $ & 62: & $ 62                     $ \\ \hline
44: & $ 66-22                     $ &     & $                        $ \\ \hline
\end{tabular}
\end{center}

\bigskip

\end{document}
--

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Newsgroups: rec.puzzles