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<latemp_subject "Between the Screws - A Logic Puzzle" />

<latemp_meta_desc "Between the Screws - A Logic Puzzle" />

<page_extra_head_elements>
<link rel="stylesheet" href="$(ROOT)/images/css/puzzles.css"
type="text/css" media="screen, projection" title="Normal" />
</page_extra_head_elements>

<h2>Introduction</h2>

<p>
I originally wrote this puzzle for the magazine of a local Role-Playing
Games’ club, back in high school. It was originally written in Hebrew, but
is presented here in its English translation.
</p>

<h2>The Puzzle Itself</h2>

<p>
When Nom the gnome went to build his new aeroplane “Little Wing”, he
ran into a funny situation when he wanted to attach the wing to the body
of the plane.
</p>

<p>
To do that, he had to use four screws in a particular order, using four
screwdrivers of four different colours - one of them green. Furthermore, each
screw had a different shape and a different length.
</p>

<p>
Your mission is to find out the order in which the screws were attached,
their lengths, shapes, and the colour of the screwdriver used for each
screw.
</p>

<ol>
<li>
The screw that the gnome used the last was longer than the screw that needed
the blue screwdriver, but was less than twice its length. (Albeit there is
a screw that is twice as long than the one needing the blue screwdriver.)
</li>
<li>
The diamond-shaped screw was screwed after the screw with the blue screwdriver,
but before the 6cm-long screw.
</li>
<li>
Only once was a shorter screw used right after a longer one.
</li>
<li>
The screw needing the red screwdriver, which isn’t the hexagonal one, was the
last. The diamond-shaped screw did not come immediately before it.
</li>
<li>
The triangular screw came before the 2cm-long screw.
</li>
<li>
The screw needing the purple screwdriver is 8 cm long, did not
follow the 2cm long screw.
</li>
<li>
The 4cm long screw was not the square-shaped one.
</li>
</ol>

<table class="logic_sayings">

<tr>
<th>Position in Time</th>
<th>Screw Length</th>
<th>Screwdriver Colour</th>
<th>Screw Shape</th>
</tr>

<tr>
<td>1st</td>
<td></td>
<td></td>
<td></td>
</tr>

<tr>
<td>2nd</td>
<td></td>
<td></td>
<td></td>
</tr>

<tr>
<td>3rd</td>
<td></td>
<td></td>
<td></td>
</tr>

<tr>
<td>4th (Last)</td>
<td></td>
<td></td>
<td></td>
</tr>

</table>

<p>
The solution can be found below.
</p>

<h2 style="margin-top: 50em">Solution</h2>

<p>
From the puzzle the following data can be directly gathered:
</p>

<ul>
<li><b>Screw lengths:</b> 2cm, 4cm, 6cm and 8cm.</li>
<li><b>Screwdriver colours:</b> green, blue, red and purple.</li>
<li><b>Screw shapes:</b> square, diamond, hexagonal, and triangular.</li>
</ul>

<p>
Based on hint #1, we can tell that the screw needing the blue screwdriver and
the final screw were either 4cm and 6cm long respectively or 6cm and 8cm
respectively, as no other allocations fulfil the hint. According to hint #2
we know that the 6cm long screw was either 3rd or 4th. If the 6cm screw was 3rd
, then the 4th screw  must be 8cm (in accordance to hint #1).  However,
then the 3rd screw must be the one needing the blue screwdriver which is
impossible according to hint #2, which means it must be at 1st or 2nd.
Therefore, the 6cm screw was the 4th screw and the blue screwdriver was used
for the 4cm screw. So far we have:
</p>

<ul>
<li>1st or 2nd - 4cm - Blue</li>
<li>2nd or 3rd - Diamond</li>
<li>4th - 6cm</li>
</ul>

<p>
All mutually exclusive.
</p>

<p>
According to hint #4 we know that the 4th screw needed the red screw driver
and that it wasn’t the hexagonal one. Therefore, we know that
<b>«4th - 6cm - red - Not Hex»</b>. Hint #4 also tells us that the diamond
shaped screw did not come immediately before it. Thus the diamond shaped screw
must have been the 2nd one, and the 4cm screw must have been the 1st. So
what we have so far is this:
</p>

<ul>
<li>1st - 4cm - Blue</li>
<li>2nd - Diamond</li>
<li>4th - 6cm - Red - Not Hexagonal</li>
</ul>

<p>
Now according to hint #3 we know that the order cannot be
<b>4cm&rarr;2cm&rarr;8cm&rarr;6cm</b> because that would mean two shorter
screws have followed two longer ones. So we have:
</p>

<ul>
<li>1st - 4cm - Blue</li>
<li>2nd - 8cm - Diamond</li>
<li>3rd - 2cm</li>
<li>4th - 6cm - Red - Not Hexagonal</li>
</ul>

<p>
According to hint #5 the triangular screw preceded the 2cm screw, so it must
have been the 1st screw. Since the 4th screw is not hexagonal screw, the
hexagonal one must therefore be the 3rd screw, and the 4th screw must be the
square screw. Thus, we have:
</p>

<ul>
<li>1st - 4cm - Blue - Triangle</li>
<li>2nd - 8cm - Diamond</li>
<li>3rd - 2cm - Hexagonal</li>
<li>4th - 6cm - Red - Square</li>
</ul>

<p>
Now all we have left to determine are the colours of the 2nd and 3rd
screwdrivers. According to hint #6 we know that the 8cm screw was used with
the purple screwdriver, so the 2nd screwdriver must have been purple and the
3rd screwdriver was green.
</p>

<p>
Our final results are:
</p>

<table class="logic_sayings">

<tr>
<th>Position in Time</th>
<th>Screw Length</th>
<th>Screwdriver Colour</th>
<th>Screw Shape</th>
</tr>

<tr>
<td>1st</td>
<td>4 cm</td>
<td>Blue</td>
<td>Triangle</td>
</tr>

<tr>
<td>2nd</td>
<td>8 cm</td>
<td>Purple</td>
<td>Diamond</td>
</tr>

<tr>
<td>3rd</td>
<td>2 cm</td>
<td>Green</td>
<td>Hexagon</td>
</tr>

<tr>
<td>4th (Last)</td>
<td>6 cm</td>
<td>Red</td>
<td>Square</td>
</tr>

</table>