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Puzzles & Problems

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DVD Smith
1243999.  Mon Jul 31, 2017 12:55 pm Reply with quote

The world's oldest known example of a puzzle is the "Stomachion", dating from the time of Archimedes, which is a collection of 14 shapes that come together to fit a square like so:



Archimedes reportedly asked how many possible arrangements there were that could form a square. It wasn't until 2003 that an answer was found:

http://www.nytimes.com/2003/12/14/us/in-archimedes-puzzle-a-new-eureka-moment.html

The puzzle has 17152 solutions, however when you cut out rotations and reflections the number goes down to 536.
(Source)

 
DVD Smith
1244001.  Mon Jul 31, 2017 1:09 pm Reply with quote

A famous example of a mathematical problem is the Seven Bridges of Königsberg, a problem devised by Euler where you had to cross the seven bridges in the Prussian city (known today as Kaliningrad) without crossing any bridge more than once.



It's more commonly seen today as the "open/closed envelope problem", where you are tasked with drawing an open/closed envelope without taking your pen off the paper and without going back over any lines. (The puzzle is only possible with the open envelope, as you'll see in a second.)



It's actually possible to predict if a shape can be drawn without taking your pen off the paper. It's all to do with the "nodes", the areas where two or more lines come together. You need to count the number of nodes with an odd number of lines connecting them, and the number of odd nodes determines if the drawing is possible or not.

  • If a shape has 0 odd nodes, it can be drawn in one line from any point on the shape.
  • If a shape has 1 odd node, it can be drawn in one go as long as you start or finish at that odd node.
  • If a shape has 2 odd nodes, it can be drawn in one go as long as you start at one and finish at the other.
  • If a puzzle has 3 or more odd nodes, it cannot be drawn without taking the pen off the paper or going over an existing line.


The closed envelope above has 4 odd nodes and so cannot be drawn in one go. However, the open envelope only has 2, and so it can easily be drawn without taking your pen off the paper.

 
'yorz
1244008.  Mon Jul 31, 2017 1:43 pm Reply with quote



Recreate this from one single piece of paper; no glue nor sticky tape.



Make this equation right by moving just one match stick.

 
DVD Smith
1244010.  Mon Jul 31, 2017 1:58 pm Reply with quote

There are a couple of answers to that matchstick one.

The supposedly "correct" answer is that you move the last stick from the top line and put it above the answer on the right to create "22/7 = π", but it's not technically right since 22/7 does not equal pi exactly.

The other "correct" version I've seen is that you remove one of the sticks from the second X on the top line to create "XIIII", which makes "14/7 = 2". But this also doesn't work because a) taking off that stick would leave "X/III", and b) 14 is never expressed as XIIII, only XIV (although oddly IIII is used for 4 on some clocks).

So my answer would be to take the final match from the top row and put it diagonally over the equals sign to create the "not equals" sign, and thus you get the correct equation "22/7 ≠ 2".

As for the other puzzle, I have no paper, but I'm guessing an optical illusion and clever lighting is involved.

 
Alfred E Neuman
1244015.  Mon Jul 31, 2017 2:06 pm Reply with quote

DVD Smith wrote:
b) 14 is never expressed as XIIII, only XIV (although oddly IIII is used for 4 on some clocks).


Not quite never, as discussed here a few times in the past, most recently over here: http://old.qi.com/talk/viewtopic.php?p=1232612#1232612

 
DVD Smith
1244023.  Mon Jul 31, 2017 2:27 pm Reply with quote

Wow, in that case I stand corrected. :)

Do we know why clock faces use IIII?

 
Alfred E Neuman
1244025.  Mon Jul 31, 2017 2:32 pm Reply with quote

DVD Smith wrote:
Do we know why clock faces use IIII?


Some years ago I posted on that, but I see I didn't link to a source. Lazy bugger...

http://old.qi.com/talk/viewtopic.php?p=737606#737606

Edit: Not only am I lazy, but I'm probably wrong too.

 
GuyBarry
1244030.  Mon Jul 31, 2017 2:55 pm Reply with quote

'yorz wrote:




Make this equation right by moving just one match stick.


How about this?

You pick up the matchstick forming the second "I" of "XXIII". Then you light it and set fire to the third "I". Finally you blow it out and put it down next to the "II".

Result: XXI / VII = III


Last edited by GuyBarry on Mon Jul 31, 2017 3:03 pm; edited 2 times in total

 
'yorz
1244032.  Mon Jul 31, 2017 2:56 pm Reply with quote

DVD Smith wrote:
my answer would be to take the final match from the top row and put it diagonally over the equals sign to create the "not equals" sign, and thus you get the correct equation "22/7 ≠ 2".

Is in general taken as the right answer.

DVD Smith wrote:
As for the other puzzle, I have no paper, but I'm guessing an optical illusion and clever lighting is involved.

Nope.

 
Dix
1244119.  Tue Aug 01, 2017 7:46 am Reply with quote

Yorz, I see how to do the paper one. Will prove it when I get home.

 
'yorz
1244130.  Tue Aug 01, 2017 8:26 am Reply with quote

Please do. :-)

 
Jenny
1244186.  Tue Aug 01, 2017 5:47 pm Reply with quote

I think I know how to do the paper one, but it only works if you photograph it from that particular angle.

 
'yorz
1244190.  Tue Aug 01, 2017 6:52 pm Reply with quote

Well - get yourself paper and scissors and....

 
Dix
1244238.  Wed Aug 02, 2017 7:43 am Reply with quote

Darn, I forgot. Will try to remember today.

 
Dix
1244313.  Wed Aug 02, 2017 3:29 pm Reply with quote

Ta-da!

 

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