Number sequences

Back from the break, with new interesting sequence I learned:

1 2 4 6 3 9 12 8 10 5…
what are the next number(s)?

This can be rather hard sequence to solve, it seems random but its actually not.
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Note: Comments may have spoilers! Come up with solution on your own before reading them.

Beer Bubbles

Did you noticed that bubbles in the glass of beer or sparkling wine are moving down initially? It is true - just carefully watch the glass as you pour liquid in, people often do not notice small things like that. It seems counter intuitive, but explanation is rather simple. What is it ?

KaleidoTile

Jeff Weeks from geometrygames.org has released Mac OS X version of KaleidoTile. Learn about polyhedra and tilings while creating colorful kinematic art. The application has colorfull and easy to use interface which allows you to manipulate and animate various parameters in intuitive way. If you have 3D stereo glasses you can view object in 3D space. KaleidoTile is very nicely done little app, its free under GPL. Check it out!

Race

Mark and Steve ran 100 meter race and Mark won, he crossed finish line when Steve was at 95 meter mark. On second race Mark started 5 meters before starting line, so he was handicapped by the exact disatnce he won first race by. Given that speed both men is the same as it was in first race who will win second race ?

Two candles

Here is simple one, you have two candles of different length. You light both of them and cover them with glass cover of some sort (doesn't really matter what the cover is). Which one will die out first, tall candle or short one? It's easy to just do this experiment and and see it on practice, however thinking about what will happen is interesting and can lead astray.
Let us know what you think!
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Note: Comments may have spoilers! Come up with solution on your own before reading them.

River Crossing

Recently I got River Crossing as present from my wife. It is nice simple travel game from ThinkFun.com. One way to find solution is by eliminating all illegal moves. Another strategy could be to find a plank that has least number of possible placements, then one with slightly larger number of placements etc, connecting these sets would lead to the solution.

The most fun however was to watch our kids solve the puzzles. One interesting observation I got from them, is the longer the plank the harder it is to rotate it ! They have no problem rotating small planks on the whim, however constatntly forgeting that long ones can be rotated just as easily. May be its psyhological perception that long planks are bigger and heavier, who wants to haul them around. Another observation is long way seeds doubt in their mind even if they are are on the right track. If there are too many moves which take them long way around the game field they begin to doubt themself and look for shorter way. Interestingly how both these obstacles interfere with our prblem solving in real life !

If you played the game and have strategy of your own, please share it here :)

6 Matches

You got 6 matches, arrange them to form four triangles. You can not break macthes in smaller pieces. Matches can only be connected at the ends, in other words you must use full length of a match.

Airplane on conveyer belt

Here is interesting question I heard the other day, while it is not new but I liked it anyway:

Can an airplane lift off the conveyer belt which is moving at opposite way with the same speed that airplane would be running along the runway? So, basically plane would remain stationary relatively to the ground.

The answer is simple once you think about it.
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Note: Comments may have spoilers! Come up with solution on your own before reading them.

Magic square or mystical ball

Here is interesting puzzle, which while simple can be impressive for feeble minds:

English variant:

http://mysticalball.com

Russian Variant:

http://www.ugbereg.ru/magic.html

Translated instructions for russian version:

1. think of any two digit number
   
2. subtract from it digits which its made of (for example if you thought of 54 you need to subtract 4 and 5, result will be 45)
3. find that number and its symbol in the table
   
4. think about that symbol
   
5. Click on large big square above the table.

How does it work ? If you want, time yourself the answer is really rather simple.

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Note: Comments may have spoilers! Come up with solution on your own before reading them.

Möbius strip

This is interesting puzzle that gives unexpected results for people unfamiliar with properties of Mobius strip. A model can be easily made from a paper strip,  half-twist one end and then joining the ends of the strip together with scotch tape to form a single strip. 

It has few interesting properties, one of which is that mobius strip has only one surface. For example, if you start drawing line from the seam in the middle of strip, it will meet the starting point and will be double the length of the original strip of paper.

Now, here is questions:

What will happen if you take scissors and cut mobius strip along the middle (or follow the line drawn as explained in the example above)? What will happen if you do it again ?

It is easy to find answers to those questions by trying out, but try to solve in your head first and then check your solution with experiment. 

Personal note, my son was amazed with results and which prompted this particular puzzle.