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