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shlomi-fish-homepage / t2 / puzzles / logic / tip-of-the-sword / index.html.wml

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#include '../template.wml'

<latemp_subject "On the Tip of the Sword - A Logic Puzzle" />

<latemp_meta_desc "On the Tip of the Sword - 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>

<div class="logic">
<h2>Introduction</h2>

<p>
I originally wrote this puzzle for the magazine of a local Role-Playing
Games’ club, back in high school. I later on slightly de-RPGed and sent it
to <a href="http://www.dellmagazines.com/">Dell Magazines</a> for
publication. I received no reply.
</p>

<h2>Note (2006-December-28)</h2>

<p>
I traced the solution and fixed the hints of the puzzle.
</p>

<h2>The Puzzle Itself</h2>

<p>
When Pierre de Fermat, the famous French mathematician, was just a
student, he had to visit the most obscure places for his studies. One
evening he was a guest at the house of an old French hero - the Marquis
François de Fougéres - who told him many tall tales about his adventurous
life.
</p>

<p>
At the beginning of the narrative, the old swashbuckler told him that during
his adventures he managed to collect a set of five luxurious swords: two
plain-tipped, two silver tipped and a very precious golden sword. One sword
was given to him as a gift by the king Henry the IV, and he found
the rest (at least as he told) in a dragon’s lair, in a pirate’s ship,
in an ancient tomb, and inside a treasure box. Each sword is of a different
type: a khopesh (an Egyptian sword), a long sword, a short sword, a rapier
(the sword of swashbucklers), and a scimitar (an Arabian sword). The warrior,
who was very proud of his collection, put it on his room’s wall, in a
horizontal row.
</p>

<p>
Once he heard that, Fermat’s interest was aroused and during the narrative
of de Fougéres he tried to find every detail given about the swords. He also
noted a couple of notes on a piece of paper which he held in his hands.
</p>

<p>
After the marquis had finished his story, Fermat could tell him the order
in which he had arranged his swords. Can you discover, according to the
following excerpts from the marquis’ story, what is the tip colour, the type
and the origin of the swords in every place, as well?
</p>

<ol>

<li>
<p>
“The first sword I found was the golden sword, which I found a month after I
had started adventuring. I put it to the left of both of the plain-tipped
swords,
so its appearance won’t be diminished. Still, it isn’t on one of the edges, so
it will stand out. In addition, I didn’t place the silvered swords adjacent to
each other.”
</p>
</li>

<li>
<p>
“Three years after the death of my comrade Damian, I have found the long sword
in the dragon’s lair. I didn’t put it in the rightmost position.”
</p>
</li>

<li>

<p>
“There is a sword, which I found in the ship of the pirate Draco ‘the Dumb’ and
which isn’t short as the pirate custom for such swords is. I placed it to
the left of another extraordinary sword. The latter was given to me as a
present by our noble king for killing Draco. Unfortunately, it wasn’t
silvered.”
</p>

<p>
“Left to the sword which I found in the pirate’s ship, is the scimitar, which
wasn’t found in the ancient tomb, and which has a plain tip.”
</p>

</li>

<li>
<p>
“Now let’s return to my collection: I have placed one of the simple swords,
the rapier, and the khopesh - in that order - one beside the other. They make
a wonderful combination!! The khopesh is also right to the short sword.”
</p>
</li>

</ol>

<table class="logic_sayings">

<tr>
<th>Place</th>
<th>Leftmost</th>
<th>Middle-Left</th>
<th>Centre</th>
<th>Middle-Right</th>
<th>Rightmost</th>
</tr>

<tr>
<td><b>Tip</b></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>

<tr>
<td><b>Type</b></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>

<tr>
<td><b>Origin</b></td>
<td></td>
<td></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>
According to hint #1, we can tell that the golden sword is in either the
mid-left or middle positions, and that the plain-tipped swords are to its
right. Now, if it were in the middle position, then the plain-tipped swords
would have to be in the mid-right and rightmost positions, and as a result,
the silver tipped swords would have to be in the mid-left and leftmost
positions. However, also according to hint #1, the silvered swords are not
adjacent to each other. Thus, the Golden sword is in the mid-left
position and one of the silvered swords is in the leftmost position.
</p>

<p>
So far we have:
</p>

<ul>
<li>Leftmost - Silvered</li>
<li>Mid-left - Golden</li>
</ul>

<p>
The golden sword was the first sword De Fougéres found and he found it
a month after adventuring. So according to hint #2, it couldn’t have been
the long sword which was found in the dragon’s lair. Furthermore, according
to hint #3, it isn’t the sword that was given to him as a present by the king.
</p>

<p>
Now, since the sword given as a present by the king was not silvered, and
cannot be the golden sword, it must be ordinary. So, so far we have:
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Plain-tipped - Present from the King - Not Scimitar</li>
<li>Pirate Ship - Not short - Not scimitar - Mid-Left, Centre or Mid-Right</li>
<li>Scimitar - Leftmost, Mid-Left or Centre - Not found in the pirate’s ship,
Not given by the king - Not found in a dragon’s lair - Not found in the
ancient tomb - Not silvered.</li>
</ul>

<p>
The scimitar has been excluded from four different origins, so it must have
been found in remaining one which is inside the treasure box. Furthermore, it is
not silvered, so it cannot be the leftmost sword, and the sword found in the
pirate’s ship should be to its right, and the sword that was given as a
present by the king to its right. Thus, we have the following associations:
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Plain-tipped - Present from the King - Not Scimitar - Mid-right or
Rightmost</li>
<li>Pirate Ship - Not short - Not scimitar - Centre or Mid-Right</li>
<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
</ul>

<p>
And integrating hint #2 into the associations:
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Plain-tipped - Present from the King - Not Scimitar - Not long sword -
Mid-right or Rightmost</li>
<li>Pirate Ship - Not short - Not long - Not scimitar - Centre or Mid-Right</li>
<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in Dragon’s Lair - Not Rightmost</li>
</ul>

<p>
And the fact that the Khopesh is right to the short sword
(according to hint #4):
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
Not Khopesh</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Plain-tipped - Present from the King - Not Scimitar - Not long sword -
Mid-right or Rightmost</li>
<li>Pirate Ship - Not short - Not long - Not scimitar - Centre or Mid-Right</li>
<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in dragon’s lair - Not Rightmost</li>
<li>Short sword - not rightmost - Not found in pirate’s ship</li>
<li>Rightmost - Not scimitar - Not long sword - Not short sword - Not found in
pirate’s ship - Not found in treasure’s box - Not found in Dragon’s Lair -
Not golden</li>
</ul>

<p>
Now let’s assume that the sword given as a present by the king is in the
mid-right position. In this case, the sword found in the pirate ship must be
in the centre position, and the scimitar will be in the mid-left position. So
we get:
</p>

<ul class="branch">
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
Not Khopesh</li>
<li>Mid-Left - Golden - Scimitar - Found in treasure box</li>
<li>Centre - Pirate Ship - Not long sword - Not short sword - Not scimitar</li>
<li>Mid-Right - Plain-tipped - Present from the King - Not Scimitar -
Not long sword</li>
<li>Long sword - Found in dragon’s lair - Not Rightmost</li>
<li>Short sword - not rightmost - Not found in pirate’s ship</li>
<li>Rightmost - Not scimitar - Not long sword - Not short sword - Not found in
pirate’s ship - Not found in treasure’s box - Not found in Dragon’s Lair -
Not golden</li>
</ul>

<p>
The long sword must be in he leftmost position, because it cannot be
anywhere else:
</p>

<ul class="branch">
<li>Leftmost - Silvered - Long sword - Found in Dragon’s Lair</li>
<li>Mid-Left - Golden - Scimitar - Found in treasure box</li>
<li>Centre - Pirate Ship - Not long sword - Not short sword - Not scimitar</li>
<li>Mid-Right - Plain-tipped - Present from the King - Not Scimitar -
Not long sword</li>
<li>Short sword - not rightmost - Not found in pirate’s ship</li>
<li>Rightmost - Not scimitar - Not long sword - Not short sword - Not found in
pirate’s ship - Not found in treasure’s box - Not found in Dragon’s Lair -
Not golden</li>
</ul>

<p>
And the short sword must be in the mid-right position:
</p>

<ul class="branch">
<li>Leftmost - Silvered - Long sword - Found in Dragon’s Lair</li>
<li>Mid-Left - Golden - Scimitar - Found in treasure box</li>
<li>Centre - Pirate Ship - Not long sword - Not short sword - Not scimitar</li>
<li>Mid-Right - Plain-tipped - Short Sword - Present from the King</li>
<li>Rightmost - Not scimitar - Not long sword - Not short sword - Not found in
pirate’s ship - Not found in treasure’s box - Not found in Dragon’s Lair -
Not golden</li>
</ul>

<p>
Since the khopesh must be right to the short sword it is in the rightmost
position, and the rapier is in the centre position:
</p>

<ul class="branch">
<li>Leftmost - Silvered - Long sword - Found in Dragon’s Lair</li>
<li>Mid-Left - Golden - Scimitar - Found in treasure box</li>
<li>Centre - Rapier - Found in Pirate Ship</li>
<li>Mid-Right - Plain-tipped - Short Sword - Given by the King</li>
<li>Rightmost - Khopesh - Found in Ancient Tomb</li>
</ul>

<p>
However, then the the Rapier and the Khopesh won’t be adjacent in accordance
to hint #4. So we now know that the sword given by the king is not in the
mid-right position, and must be in the rightmost one:
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
Not Khopesh</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Rightmost - Plain tipped - Given by the King - Khopesh or Rapier</li>
<li>Pirate Ship - Not short - Not long - Not scimitar - Centre or Mid-Right</li>
<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in Dragon’s Lair - Not Rightmost</li>
<li>Short sword - not rightmost - Not found in pirate’s ship</li>
</ul>

<p>
Since the rightmost sword is a Rapier or a Khopesh then according to hint #4,
it cannot be the Rapier because the Rapier is in the middle of a three-swords
sequence. So it must be the Khopesh, and the sword to its immediate right
(mid-right position) is a Rapier, and the sword to the latter’s left, must be
a plain tipped sword. So we get the following associations:
</p>

<ul>
<li>Leftmost - Silvered - Not given by the king - Not
found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
Not Khopesh</li>
<li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
dragon’s lair</li>
<li>Centre -Plain Tipped</li>
<li>Mid-right - Rapier</li>
<li>Rightmost - Plain tipped - Given by the King - Khopesh</li>
<li>Pirate Ship - Rapier or Khopesh - Centre or Mid-Right</li>
<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in Dragon’s Lair - Not Rightmost</li>
<li>Short sword - not rightmost - Not found in pirate’s ship</li>
</ul>

<p>
The sword found in the pirate’s ship must be the rapier because the khopesh
was given by the king. Furthermore, it is silver-tipped as mid-right is the
only place left for the second silver-tipped sword:
</p>

<ul>

<li>Leftmost - Silvered - Not found in a Pirate’s ship - Not found in a
treasure box - Long sword or short sword</li>
<li>Mid-Left - Golden - Short sword or Scimitar- Not found in
dragon’s lair</li>
<li>Centre - Plain Tipped</li>
<li>Mid-right - Silver tipped - Found in pirate ship - Rapier</li>
<li>Rightmost - Plain tipped - Given by the King - Khopesh</li>


<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in Dragon’s Lair</li>
<li>Short sword - Leftmost or Mid-Left</li>

</ul>

<p>
The only origin left for the short sword is the ancient tomb:
</p>

<ul>

<li>Leftmost - Silvered - Not found in a Pirate’s ship - Not found in a
treasure box - Long sword or short sword</li>
<li>Mid-Left - Golden - Short sword or Scimitar- Not found in
dragon’s lair</li>
<li>Centre - Plain Tipped</li>
<li>Mid-right - Silver tipped - Found in pirate ship - Rapier</li>
<li>Rightmost - Plain tipped - Given by the King - Khopesh</li>


<li>Scimitar - Found in treasure box - Mid-Left or Centre - Not silvered</li>
<li>Long sword - Found in Dragon’s Lair</li>
<li>Short sword - Found in the Ancient Tomb - Leftmost or Mid-Left</li>

</ul>

<p>
The scimitar has a plain tip (according to hint #3) so it cannot be positioned
in the mid-left. So it must be in the centre. So the mid-left sword
must be the short sword, and the leftmost one the long sword:
</p>

<ul>
<li>Leftmost - Silvered - Long Sword - Found in Dragon’s Lair</li>
<li>Mid-Left - Golden - Short Sword - Found in an ancient tomb</li>
<li>Centre - Plain tipped - Scimitar - Found in treasure box</li>
<li>Mid-Right - Silvered - Found in Pirate Ship - Rapier</li>
<li>Rightmost - Plain tipped - Present from the king - Khopesh</li>
</ul>

<p>
So, to summarise the results, the solution is:
</p>

<table class="logic_sayings">

<tr>
<th>Place</th>
<th>Leftmost</th>
<th>Middle-Left</th>
<th>Centre</th>
<th>Middle-Right</th>
<th>Rightmost</th>
</tr>

<tr>
<td><b>Tip</b></td>
<td>Silver</td>
<td>Golden</td>
<td>Plain</td>
<td>Silver</td>
<td>Plain</td>
</tr>

<tr>
<td><b>Type</b></td>
<td>Long Sword</td>
<td>Short Sword</td>
<td>Scimitar</td>
<td>Rapier</td>
<td>Khopesh</td>
</tr>

<tr>
<td><b>Origin</b></td>
<td>Dragon’s Lair</td>
<td>Ancient Tomb</td>
<td>Treasure Box</td>
<td>Pirate Ship</td>
<td>Present from the King</td>
</tr>

</table>


#if 0
# <p>
# ===============================================================
# </p>
#
# <p>
# Now let’s assume that the scimitar is in the centre position. This way, the
# sword found in the pirate ship must be in the mid-right position, and the
# sword that was given as a present by the king must be in the rightmost
# position. So we get:
# </p>
#
# <ul style="border: 1pt dashed black;">
# <li>Leftmost - Silvered - Not given by the king - Not
# found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
# Not Khopesh</li>
# <li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
# dragon’s lair</li>
# <li>Centre - Scimitar - Found in treasure box - Not silvered</li>
# <li>Mid-Right - Pirate Ship - Not short - Not long - Not scimitar</li>
# <li>Rightmost - Plain-tipped - Present by the king - Not scimitar -
# Not long sword - Not short sword</li>
# </ul>
#
# <p>
# So the Mid-right sword is the only one that is left to be the second silvered
# sword:
# </p>
#
# <ul style="border: 1pt dashed black;">
# <li>Leftmost - Silvered - Not given by the king - Not
# found in a Pirate’s ship - Not found in a treasure box - Not scimitar -
# Not Khopesh</li>
# <li>Mid-Left - Golden - Not given by the king - Not long sword - Not found in
# dragon’s lair</li>
# <li>Centre - Scimitar - Found in treasure box  - Plain tipped</li>
# <li>Mid-Right - Pirate Ship - Silvered - Rapier or Khopesh</li>
# <li>Rightmost - Plain-tipped - Present by the king - Rapier or Khopesh</li>
# </ul>
#
# <p>
# And the Leftmost sword must be the long sword and the mid-left one must be the
# short sword:
# </p>
#
# <ul style="border: 1pt dashed black;">
# <li>Leftmost - Silvered - Long Sword - Not given by the king - Not
# found in a pirate’s ship - Not found in a treasure box</li>
# <li>Mid-Left - Golden - Short Sword - Not given by the king - Not found in
# dragon’s lair</li>
# <li>Centre - Scimitar - Found in treasure box  - Plain tipped</li>
# <li>Mid-Right - Pirate Ship - Silvered - Rapier or Khopesh</li>
# <li>Rightmost - Plain-tipped - Present by the king - Rapier or Khopesh</li>
# </ul>
#
# <p>
# And we can fill in more details:
# </p>
#
# <ul style="border: 1pt dashed black;">
# <li>Leftmost - Silvered - Long Sword - Found in dragon’s Lair</li>
# <li>Mid-Left - Golden - Short Sword - Found in an ancient tomb</li>
# <li>Centre - Plain tipped - Scimitar - Found in treasure box</li>
# <li>Mid-Right - Silvered - Found in Pirate Ship - - Rapier or Khopesh</li>
# <li>Rightmost - Plain tipped - Present by the king - Rapier or Khopesh</li>
# </ul>
#endif

</div>