Following this blog

If you are following this blog by waiting for it to appear on my 'super-feed' then I'm going to recommend you switch to following this blog's RSS feed directly. This is because it takes up to an hour for my new posts to appear in my Google Reader, at which point I can then add them manually to my super-feed - if I'm still logged in. This means you might not get any notification of a new post for several days...

Actually, after spending 20 seconds thinking about it, I've decided that this will be the last post I will mark in my 'super-feed' - please subscribe to this blog's feed to continue reading :)

Praha

Prague, or Praha as it's also known, is a fascinating place. It's the capital city of the Czech Republic. It's hard to believe that only 20 or so years ago the main square (well, one of them) was the scene of violent anti-communism riots. I've walked up streets that had Russian tanks rolling down them 40 years ago. The Museum has obvious repairs from where the Soviet tanks fired at it, thinking it was the Parliament building! The role of Czech/Slovakia within the context of the Cold War is fascinating - check it out on Wikipedia or somesuch if you're interested.

I like Praha. It's got a real character to it. The people are modern. The city has some truly beautiful spots. The language, although almost completely impossible for me to understand, sounds clear and intelligent. The food is honest and satisfying. The beer is FANTASTIC.

We had one great day of weather, and a couple of rather lousy ones. However I'm starting to appreciate grey skies and light rain - it keeps the hordes of (other) tourists at bay, and makes photographs easier to compose (no bright sunshine to ruin the balance).

Today we visited the Bone Church in Kutná Hora - a fascinating place, filled with the bones of many thousands of (quite dead) people. Check it out here:
http://en.wikipedia.org/wiki/Kutn%C3%A1_Hora

I'll post some photos at some stage. We're heading into the mountains tomorrow, as well as a visit to Aushwitz Death Camp - that will be sobering. Then on to Krakow in Poland.

Central Europe Week 1 - Vienna to Cesky Krumlov

Today marks approximately one week since we departed for Central Europe. So far, it's been a very interesting experience - not entirely without worry although so far all problems have been resolved. Except our flight on Alitalia in two weeks which might not happen if the airline ceases to exist before then...

After four aircraft flights from Wellington to Vienna, Austria, we finally arrived on Monday evening. Unfortunately, the same cannot be said for P's luggage. After waiting around for 30 minutes just in case, we filed a missing luggage report with the airline and hit the bus into Vienna.

We stayed for two nights at a very simple but pleasant 'pension' (apartment-style accomodation) in the west of the city. Situated right near a major U-bahn (underground) station and trams, getting around was no problem at all.

P's luggage turned up on the third day - you can imagine our relief. The airline customer support was pretty bad - the phone number to call would put you through then disconnect you because they were 'busy' - no holding! Also, making collect calls is unheard of here for some reason. We couldn't even get an international operator.

Then we joined our Intrepid tour and stayed in another pension in the north-west. This place was pretty terrible actually - the sink wouldn't drain, the fridge didn't work, the shower head was broken, the lightswitches were hanging out of the wall. But it was fun and we didn't die.

In the interests of making this interesting, here are the highlights:

• Schoenbrunn Palace - ridiculously huge Baroque-style castle/mansion with ridiculously huge gardens.
• Upper Belvedere art gallery - we saw Gustav Klimt's "The Kiss", which was actually quite entrancing. P stayed longer and I went to:
• Vienna Natural History Museum. Wow. I spent an hour just looking at rocks. Interesting and beautiful rocks though. But a lot of them. 1500 or so? 700 meteorites, an entire floor of stuffed animals (birds, fish, mammals, reptiles, the works). The highlight was the Venus of Willendorf - the first known example of human art, dated around 25,000 years ago.
• The catacombs beneath the cathedral - lots of bones. LOTS of bones. Creepy.
  
• A lot of other stuff. There's so much to do in Vienna it's crazy.

We also spent half a day in Bratislava, the capital city of Slovakia. That was an interesting journey but I have to say it's not an interesting city at all.

Yesterday we arrived in Cesky Krumlov, a picturesque little town between Salzburg and Prague. It's a really charming place. We had a tour from a resident who explained the significance of sights around the town, as well as her experiences during communism. Then we had a tour of the castle which is full of remarkable frescos, some more than 400 years old.

It's only been a week but we're having a total blast. Our Intrepid leader is excellent, the group gets along well, and the locals are usually friendly (although not so much in Vienna, unfortunately).

Tomorrow we head to Prague for a few days, then on to Poland!

Korg Kontrol49 & Akai MPK49 Comparison

This review has been moved here.

New hybrid heli

A new kind of hybrid helicopter perhaps?

(Not my photo - found it on RunRyder.com. Don't know who owns copyright).

Solution

Although thousands of readers pitted themselves against this challenge, obviously none were able to solve this puzzle, judging by the comments left.

Here is one solution I came up with. I have seen at least two other valid yet different solutions, so this is by no means the only valid answer.

 U = unknown stone
 N = known 'normal' stone.
 H = Heavy
 L = Light

 WEIGH [U,U,U,U] against [U,U,U,U]
 IF scales balance:
   LABEL weighed stones N
   LABEL remaining four stones a,b,c,d
   WEIGH [a,b] against [c,N]
   IF scales balance:
     WEIGH [d] against [N]
     IF scales tip towards [d]     -> SOLUTION (d = H)
     ELSE (scales tip towards [N]) -> SOLUTION (d = L)
   ELSIF scales tip towards [a,b]:
     WEIGH [a] against [b]
     IF scales balance             -> SOLUTION (c = L)
     ELSIF scales tip towards [a]  -> SOLUTION (a = H)
     ELSE (scales tip towards [b]) -> SOLUTION (b = H)
   ELSE (scales tip towards [c,N]):
     WEIGH [a] against [b]
     IF scales balance             -> SOLUTION (c = H)
     ELSIF scales tip towards [a]  -> SOLUTION (b = L)
     ELSE (scales tip towards [b]) -> SOLUTION (a = L)
 ELSE:
   LABEL unweighed stones N
   LABEL 'heavier' weighed stones e,f,g,h
   LABEL 'lighter' weighed stones i,j,k,l
   WEIGH [e,f,i] against [g,j,N]
   IF scales balance:
     WEIGH [k] against [l]
     IF scales balance             -> SOLUTION (h = H)
     ELSEIF scales tip towards [k] -> SOLUTION (l = L)
     ELSE (scales tip towards [l]) -> SOLUTION (k = L)
   ELSIF scales tip towards [e,f,i]:
     WEIGH [e] against [f]
     IF scales balance             -> SOLUTION (j = L)
     ELSEIF scales tip towards [e] -> SOLUTION (e = H)
     ELSE (scales tip towards [f]) -> SOLUTION (f = H)
   ELSE (scales tip towards [g,j,N]:
     WEIGH [g] against [N]
     IF scales balance             -> SOLUTION (i = L)
     ELSE (scales tip towards [g]) -> SOLUTION (g = H)


Note that the solution space does not include all possible states for all twelve stones, because labelling is performed after the first weigh, which excludes some combinations.



Details:
========
========

12 stones, labelled a-l, such that any one single stone may be the different one - heavier (H) or lighter (L) than a 'normal' (N) stone.

 a b c d e f g h i j k l
 N N N N N N N N N N N N
 H H H H H H H H H H H H
 L L L L L L L L L L L L



* WEIGH(1) any eight stones:


   N N N N   N N N N
   H H H H   H H H H
   L L L L   L L L L
  -------------------
           ^

There are two possible outcomes:


A: The scales balance, leaving FOUR unknown and EIGHT normal stones.

   N N N N   N N N N    N N N N
  ------------------- + H H H H
           ^            L L L L

B: The scales tip, leaving FOUR possible N or H, FOUR possible N or L and FOUR normal stones.

   N N N N   N N N N
   H H H H   L L L L
  _________.--------- + N N N N
           ^


Scenario A:
===========
 - relabel unknown stones a-d
 - FOUR unknown and EIGHT normal stones:

 a b c d
 N N N N N N N N N N N N
 H H H H
 L L L L


* WEIGH(2) stones a-c with one normal stone:

   a b           c
   N N           N N
   H H           H      d
   L L           L      N
  ------------------- + H
           ^            L

There are three possible outcomes:

AA: The scales balance, leaving ONE unknown stone d.

   a b           c      d
   N N           N N    N
  ------------------- + H
           ^            L


AB: The scales tip towards a & b, leaving THREE unknown stones a,b,c.

   a b           c
   N N           N N
   H H           L      d
  _________.--------- + N
           ^
 - a & b cannot be L
 - c cannot be H
 - d is known to be normal.


AC: The scales tip towards c, leaving THREE unknown stones a,b,c.

   a b           c
   N N           N N
   L L           H      d
  ---------._________ + N
           ^
 - a & b cannot be H
 - c cannot be L
 - d is known to be normal.



Scenario AA:
============
 - ONE unknown stone and ELEVEN normal stones:

 a b c d
 N N N N N N N N N N N N
       H
       L


* WEIGH(3) stone d against a normal stone:

   d
   N   N
   H
   L
  -------
     ^
 - if scales tip towards d => d is H
 - if scales tip towards N => d is L


Scenario AB:
============
 - THREE unknown stones and NINE known stones:

 a b c d
 N N N N N N N N N N N N
 H H L


* WEIGH(3) stone a against b:

   a   b
   N   N
   H   H
  -------
     ^
 - if scales balance => c is L
 - if scales tip towards a => a is H
 - if scales tip towards b => b is H



Scenario AC:
============
 - THREE unknown stones and NINE known stones:

 a b c d
 N N N N N N N N N N N N
 L L H

* WEIGH(3) stone a against b:

   a   b
   N   N
   L   L
  -------
     ^
 - if scales balance => c is H
 - if scales tip towards a => b is L
 - if scales tip towards b => a is L




Scenario B:
===========
 - relabel unknown stones e-l
 - FOUR possible N/H, FOUR possible N/L and FOUR normal stones:

 e f g h i j k l
 N N N N N N N N N N N N
 H H H H L L L L


* WEIGH(2) e,f,i,g,j and ONE normal stone:

   e f i       g j
   N N N       N N N
   H H L       H L      h k l
  ------------------- + N N N
           ^            H L L


There are three possible outcomes:

BA: The scales balance, leaving THREE unknown stones h,k,l:

   e f i       g j
   N N N       N N N
                        h k l
  ------------------- + N N N
           ^            H L L

 - e,f,i,g,j must be normal


BB: The scales tip towards e,f,i, leaving THREE unknown stones e,f,j:

   e f i       g j
   N N N       N N N
   H H           L      h k l
  _________.--------- + N N N
           ^
 - h,k,l must be normal
 - i cannot be L
 - g cannot be H


BC: The scales tip towards g,j, leaving TWO unknown stones i,g:

   e f i       g j
   N N N       N N N
       L       H        h k l
  ---------._________ + N N N
           ^
 - h,k,l must be normal
 - e,f cannot be H
 - j cannot be L


Scenario BA:
============
 - ONE possible N/H and TWO possible N/L

 e f g h i j k l
 N N N N N N N N N N N N
       H     L L

* WEIGH(3) k,l:

   k   l
   N   N
   L   L
  -------
     ^
 - if scales balance => h is H
 - if scales tip towards k => l is L
 - if scales tip towards l => k is L


Scenario BB:
============
 - TWO possible N/H and ONE possible N/L

 e f g h i j k l
 N N N N N N N N N N N N
 H H       L

* WEIGH(3) e,f:

   e   f
   N   N
   H   H
  -------
     ^
 - if scales balance => j is L
 - if scales tip towards e => e is H
 - if scales tip towards f => f is H


Scenario BC:
============
 - ONE possible N/H and ONE possible N/L

 e f g h i j k l
 N N N N N N N N N N N N
     H   L

* WEIGH(3) g and ONE normal stone:

   g
   N   N
   H
  -------
     ^

 - if scales balance       => g must be N, so i is L
 - if scales tip towards g => g must be H

Comments are, of course, welcome.

The Twelve Stones Puzzle

There are 12 visibly identical stones, 11 of equal weight, 1 of unequal weight (either heavier or lighter).

Using no more than three weighings on a simple balance scale, determine which stone has a different weight and whether it is heavier or lighter.