New site is up and running!

Finally I have migrated over to new site!

See you there!

There will be no more posts on this blogs, this is the last one. Update your RSS feeds and come to new home.

Curling…

First an update:
I have not forgot or abandoned this blog :)
But I'm in the midst of working on new home for it, and I have big back log of puzzles accumulated…

Here is intersting observation in relation to passed olympics:

If you put glass upside down and then give it a clockwise spin and slide it straight forward along the dry surface (bar stand for example) then glass will tend to go left. However if surface is wet it will tend to go right. Why is that ?

Traveling Ant

Here is one of numerous Gardner puzzles:

Imagine elastic rope 1 meter long, an ant start moving with speed of 10 centimeters per second from one end of the rope. He moves steadily with constant speed. Every second someone stretches the rope to increase it's length by 1 meter uniformly. Will ant ever make it to the other end of the rope?

this one is rather interesting, try to prove your answer!

Alive and kicking

Got distracted with work, travel and life as usual but fear not this blog isn't dead I still collect interesting problems. Without further ado:

You have four numbers: 3,3,3,3 (four threes) using simple operations such as +, -, *, /, (addition, subtraction, devision and multiplication) produce expressions that result in numbers from 0 to 10.
For example: 3 / 3 - 3 / 3 = 0.
Note, that you must use all four 3s in each expression. Have fun!

This is very simple and relaxing puzzle that you can solve with your kids and I have tons of fun solving with my eight year old.

Guilloché pattern and other Web apps

Here is nice Guilloché pattern generator done as web app. These patterns have long history and were used as ornaments by crafters. Wikipedia article about Guilloché is here.

The site has plenty interesting information about geometry, patterns, etc. For exampe a Butterfly curves web application.

Multiplication with your fingers

Here is interesting trick to multiply numbers in second half of multiplcation table (6-10). I do not recall where I learned it from but it has been around for quite some time. Best way to explain how it works is on example:

to multiply 6 by 7 you open 1 finger on one hand (6-5 = 1) and 2 fingers on another (7-5 = 2), then you multiply number of closed fingers on your hands and add it to sum of open fingers multiplied by 10. In our case -

4 (closed fingers on one hand) x 3 (closed fingers on another hand) + (1 + 2) * 10 = 42

another example:

8*9 translates to : 2*1 + (3+4) * 10 = 72

:)

Lost in the forest

Here is puzzle I heard on some radio or podcast show:

You are in the forest. Two trees are marked in some way. You are given rope which length is twice the distance between marked trees. The task is to find third tree that forms right triangle (triangle that has one angle of 90 degree).

There are few possible solutions here.

Relativity

Here is interesting question, while it's simple for people familiar with theory of relativity, imagining the followed experiment can be an eye openinig experience,

Imagine following device, the laser pointed straight up with a mirror mounted some distance above it that bounces light back to the laser where receptive is attached sensor. Knowing distance of round trip and time between sending light impulse and receiving it we can verify speed of light. Now lets place that device on very fast moving train. For the observer on the train nothing changes same data, same result. However for observer on the ground light now travels along zigzag or two sides of triangle covering more distance then in stationary case. Given that speed of light is the same in both cases, how is that possible?

Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences is free searchable library of various integer sequences. While site is mostly dry and blant from UI point of view, it’s content that is most fastinating. You can search for various sequences and results can be represented as graphs or sounds and include links to relevant literature. Seraching for numbers from previous quiz will reveal the sequence

(I normally do not give away answers unless there is a post solving the puzzle. But in thi particular case the gIven sequence in the previous post is very hard to solve, still you can try solving it yourself and then look it up in encyclopedia).

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.
--
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!
--
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.
--
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.

--
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.

Pants or no pants

On last episode of MathFactor podcast there was an interview with Prof Ed Burger of Williams College where he discussed interesting puzzle:

Imagine that you have a rope, one end of which is tightly tied to your left ankle and another to your right ankle. So rope and your legs form a loop. Is that possible to remove your pants (or shorts) then turn them inside out and put them back on (in the "inside out form") without breaking the loop ?
--
Note: Comments may have spoilers! Come up with solution on your own before reading them.