Can you think "outside the box?" test...

[Reticuli]

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Okay, here is a test... Has anyone taken this test? Can we really think "outside the box?"

The rules:

In regards to the above set of dots, you must connect all 9 dots with only 4 straight lines WITHOUT taking your pen/pencil off the paper...

Have fun,
Me :p

[The Supreme Canuck]

Got it.

Spoiler:

Start on the top right dot. Draw a diagonal line to the bottom left dot through the middle one. Draw up through the two above dots and keep going. Draw a diagonal line through the top middle and right middle dots. Keep going. Draw a line through the remaining dots.

[The_Radiation_Specialist]

Heres a drawing. *SPOILER*

[The Supreme Canuck]

Yep. That'll do it. I see you went in the other direction.

[paulie jay]

Got it too, just started fro a different position :)

[S.Dicenza]

Here's another way, which might be considered cheating, though it seems to follow the instructions(you end up drawing more than 4 lines, but end up with only 4 lines on the paper):

I'll start at the upper right dot. Draw a line to the left dot, then draw dawn to the bottom left dot, then again to the bottom right dot. Then redraw over the line you just made back to the bottom left dot, then up the line on the left to the middle dot, then draw a line over to the right middle dot. You end up with the letter E.

[01101001]

You can do it with one very fat line. Outside the box enough?

[TheBlackCat]

I did it in 3 lines..

[Van Rijn]

Here's another way, which might be considered cheating, though it seems to follow the instructions(you end up drawing more than 4 lines, but end up with only 4 lines on the paper):


That was my first take on it: There was no restriction against retracing a line, and there are several ways they can be connected by four lines.

[Van Rijn]

You can do it with one very fat line. Outside the box enough?


Another way to do one line: Fold the paper along three lines of dots, and three more folds between the lines. Fold like an accordion so all dots are together (three sets of three touching dots). Draw one line along the edge of the paper, across the nine dots.

Edit to add: It occurs to me that with two additional folds, it should be possible to connect all 9 dots with no lines.

[TheBlackCat]

Here is how I did it. Start at the upper left (it doesn't matter what corner, this is just an example). Draw down a long way. Then draw so that you end at a point in line with the third column but way above it. Then draw down to the bottom of the third column. As long as either your lines or the three points are not infintiely small, if you start the second line low enough and end it high enough it will pass through the three points in the middle column. This is becase the longer you make the second line, the closer it gets to being vertical. If you make it close enough to vertical it will tough the three points in the center column. You can see it here (http://img.photobucket.com/albums/v89/toddrme/puzzlesolution.jpg) (note I rotated it clockwise 90 degrees). If the dots were smaller, you can simply make the line larger. If the dots were infinitely small the line still has thickness, so this would still work.

[Tog_]

One of the programs I use at work has thi puzzle as it's logo...

[Taks]

If the dots were smaller, you can simply make the line larger. If the dots were infinitely small the line still has thickness, so this would still work.unless you assume a true point and a true line. the point is dimensionless, and the line has no width.

taks

[Van Rijn]

unless you assume a true point and a true line. the point is dimensionless, and the line has no width.

taks

But the rules didn't say that. When thinking outside the box, one should assume something can be done unless it is specifically forbidden.

[mugaliens]

Accelerate the diagram to an appreciable percentage of lightspeed, along an axis diagonal to the box. After it's compressed, draw whatever lines you like.

True, a line of infinate thickness would work, too...

[Maksutov]

Think outside the box?

No problem...

http://img128.imageshack.us/img128/6152/thinkoutsidethebox1ad.th.jpg (http://img128.imageshack.us/my.php?image=thinkoutsidethebox1ad.jpg)

although it does get a little chilly in the winter.


PS: I first saw that puzzle back in the 1960s.

[antoniseb]

I don't think I'd have gotten it if I hadn't seen it pretty often in puzzle books.

[TheBlackCat]

unless you assume a true point and a true line. the point is dimensionless, and the line has no width.

taks
Right, which is why I specified at least one of the two must be of finite size. We were told to connect a specific set of dots in the OP, all of those dots were of finite size.

[Van Rijn]

By the way, this reminds me of a bit I read some time ago on "outside the box" thinking. There is a test question that says:

You are given a barometer. How do you determine the height of a certain building?

The expected answer would be to measure the air pressure on the ground and at the top of the building and calculate from there, but there are some other answers:

Use the barometer as a weight on the end of a strong, non-stretching line. From the roof, lower the barometer to the ground. Mark the length of the line, and measure it.

Drop the barometer from the roof. Determine the time it takes to hit the ground. Given the time and acceleration, calculate the height of the building.

Find a building official and say "I'll give you this nice barometer if you tell me how tall the building is."

[The Supreme Canuck]

Heck, you could use the shadow of the building, the shadow of the barometer, and trig.

[TrAI]

Hmmm... Lets see... How about this?



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After all, there were no specified restriction on curved lines,
only that we should use only four straight ones, of course,
if you count a curved line as an infinite amount of infinitly
small straight lines, this approach does not work. ;-p

[Taks]

But the rules didn't say that. When thinking outside the box, one should assume something can be done unless it is specifically forbidden.true.
taks

[Taks]

Right, which is why I specified at least one of the two must be of finite size. We were told to connect a specific set of dots in the OP, all of those dots were of finite size.i realize that, too...

taks

[hhEb09'1]

Use the barometer as a weight on the end of a strong, non-stretching line. From the roof, lower the barometer to the ground. Mark the length of the line, and measure it.Swing the barometer, and time the period of the pendulum--that'll give you the length.

[mugaliens]

You are given a barometer. How do you determine the height of a certain building?

Use the barometer to mark a 45 degree angle, with the horizontal length equal to the height. Using the angle, find the point on the ground where the top of the building is equal to the distance from it's center. Pace off the distance, and you have the height of your building.

[HenrikOlsen]

By the way, this reminds me of a bit I read some time ago on "outside the box" thinking. There is a test question that says:

You are given a barometer. How do you determine the height of a certain building?

The expected answer would be to measure the air pressure on the ground and at the top of the building and calculate from there, but there are some other answers:

Use the barometer as a weight on the end of a strong, non-stretching line. From the roof, lower the barometer to the ground. Mark the length of the line, and measure it.

Drop the barometer from the roof. Determine the time it takes to hit the ground. Given the time and acceleration, calculate the height of the building.

Find a building official and say "I'll give you this nice barometer if you tell me how tall the building is."
Use the barometer as a weight on the end of a strong, non-stretching line.
Set it swinging, time the oscillations, calculate length from that.

Put a container of water at the bottom, measure it's temperature, drop the barometer into the container, measure the new temperature, calculate the increase in energy, calculate the height based on lost potential energy of the barometer.

Measure the length of the buildings shadow, measure the length of the barometer's shadow at the same time, use proportions to calculate the height, in barometers.

Using the barometer as a pendulum, measure the difference in frequency of the oscillations, calculate difference in gravity, and thus difference in height.

[TheBlackCat]

Stick the barometer in a rubber ball with known elastic properties. Drop it off the building ball-down. Count the number of bounces it takes before it stops and use that to compute the original drop. You could also set up a trampoline on the ground to do the same thin if you correct for the height of the trampoline. You could also set up a viscous solid material with known properties like silly puddy or ballistic geletin on the ground, drop the barometer on it, and measure the dent made. You could also use a highly bouyant liquid that the barometer is neutrally bouyant in and that has known viscosity, put it on the ground, the measure how far the barometer travels before coming to a stop. If it was less bouyant you could measure how long it takes for the barometer to reach terminal velocity. If it is more boyant you could measure how long it takes for the barometer to start heading back up. You could also have a series of sheets of paper (or some other breakable material) with various known strength, then determine what the strongest sheet of paper tha barometer can break through when dropped of the building (you could also use a varying number of sheets of a single type of paper). This assumes that the building is not tall enough for the barometer to reach terminal velocity from the air. You could always pump all the air out of the city block the building is in, or at least greatly reduce air pressure, or move the building to a high altitude or another planet.

If it is a mercury barometer you can lay it on the ground and bounce a laser off it from the height of the building, then measure how long it takes for the laser to return. You might also be able to do this with microwaves.

Throw the barometer forward off the building at a known velocity. Measure how far it travelled when it hit the ground. Correct for wind resistance, then use this to measure how long it was travelling horizontally, which is also how long it took to fall. Correct for terminal velocity of need be.

If it is an alcohol barometer and there is no wind, break the alcohol baramoter and set it on the ground. Wait for the fumes to diffuse, then compare the concentration of the alcohol fumes at the bottom edge of the building and at the top. This will tell you how far it the fumes have diffused. Alternatively you can measure how long it takes for the fumes to reach the top of the building, which will tell you the same thing.

If it is an alcohol thermometer, light the alcohol on fire and measure how long it takes for the smoke to reach the top of the building. Alternatively, measure the intensity of the light from the fire right next to it to the intensity of light at the top of the builidng, then use the inverse-square law.

Throw the barometer in the air. Measure how much force it requires for the barometer to reach the peak of its trajectory right at the top of the building.

Seal the barometer and use it as a thermometer to measure the change in temperature.

If it has any metal (or it if is mercury), connect a wire to it, then connect the other end of the wire to a radio antenna. Set up a plane-polarized radio transmitter a known distance from the building. Rotate the barometer between perpendicular to the wave front and parrallel to it. The angle of the maximum repection is the angle at which the barometer is perfeclty perpendicular to the wave front, telling you the direction of the transmitter, allowing you to use the pythagorean theorem to determine the height of the building.

You could shoot the barrelt out of an extremely powerful mass driver. If you shoot it at the ground close enough to the building and at a high enough velocity that gravitational acceleration can be neglected, you can fire it at a specific angle, then measure how far from the building it hit the ground or the angle at which it hig the ground, then use trigonometry to determine the building's height.

You can shoot it or throw at an angle into the air, then measure how far the from the building the peak of its trajectory is and how far from the building it hit the ground. The distance it took before it reached its peak will be longer, equal, or shorter than the distance it travelled after it reached its peak, depending on how hight the point of impact is relative the the building. If you know the height of the ground where it hit relative to the height the ground at the building, you can use this assymetry to determine the height of the building.

This is all I can think of right now.

[Reticuli]

I've only seen this test with one answer, however all of you found different ways, truly thinking "outside the box!" Cute picture of the thinking man outside a box... :)

Me

[The_Radiation_Specialist]

By the way, this reminds me of a bit I read some time ago on "outside the box" thinking. There is a test question that says:

You are given a barometer. How do you determine the height of a certain building?

The expected answer would be to measure the air pressure on the ground and at the top of the building and calculate from there, but there are some other answers:

Use the barometer as a weight on the end of a strong, non-stretching line. From the roof, lower the barometer to the ground. Mark the length of the line, and measure it.

Drop the barometer from the roof. Determine the time it takes to hit the ground. Given the time and acceleration, calculate the height of the building.

Find a building official and say "I'll give you this nice barometer if you tell me how tall the building is."

capture the building official and tie him on the chair. Then threaten to push the barometer up his $#@ if he doesnt tell you how high the building is... oops :o

[TheBlackCat]

Yeah, I had a couple like that but I thought if I posted them I might get a visit from the DHS.

Just don't ask.

[Argos]

I know the answer for having taken this test some 20 years ago (I failed then).

[mugaliens]

Put the barometer into a time capsule, along with a note asking future time travellers to look up how tall the building was and zap you the answer back through time to about five minutes from now.

[Joff]

Here's another "dotty" puzzle:

Given the following 12 points:

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* * * *
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* *
join them with only 5 straight lines drawn without lifting the pen etc.

Tough version: start with the pen on one of the inner 4 dots.

[TheBlackCat]

Here is one solution for the easy version: solution 1 (http://img.photobucket.com/albums/v89/toddrme/puzzle2solution.jpg). Start at either one of the top two points.

[Joff]

Here is one solution for the easy version: solution 1 (http://img.photobucket.com/albums/v89/toddrme/puzzle2solution.jpg). Start at either one of the top two points.

Well done TBC - of course by rotation that works for any of the 8 outer points. Now how about the tough version?

[TheBlackCat]

I got the hard version. You can see it Here (http://img.photobucket.com/albums/v89/toddrme/puzzle2solutions2.jpg). The top three diagrams are 3 additional solutions to the basic version. The bottom drawing is a solution the hard version. The key, apparently, is that no point has more than one line passing through it. For the 4 solutions I have to the basic version, note that the original solution and the far left solution are variations on the same basic idea while the middle and right solutions are also variations on the same basic idea.

[Joff]

Great job. My solution to the tough version was basically your top-middle path, where with minor adaptation the path can start on the top right of the inner points.

Not revisiting points is therefore not a requirement for the tough solution, although it would be one hell of an additional constraint.

[ggremlin]

I did it in one line, does a 6 inch paint brush count?

[Joff]

Well done, how are you going to get the paint off your monitor? ;)

[The Mangler]

Use the barometer as a weight on the end of a strong, non-stretching line.
Set it swinging, time the oscillations, calculate length from that.
Or just measure the string. ;)

[ggremlin]

Well done, how are you going to get the paint off your monitor? ;)

I used varnish so I could see the results! ;)

[mugaliens]

New box to think outside of:

You have a perfect string (no stretch) that's snug around a perfect planet ()no squeeze). You increase the length of the string by 1 inch then pull up. How high off the ground will you lift the string?

[The_Radiation_Specialist]

You have a perfect string (no stretch) that's snug around a perfect planet ()no squeeze). You increase the length of the string by 1 inch then pull up. How high off the ground will you lift the string?

half an inch?

[hhEb09'1]

half an inch?But you could do that by pinching and tightening the rest of the string, and pulling up the one inch loop. Letting the rest of the string loose, you can go much higher. I used a simple excel spreadsheet solver (assuming a spherical planet about the size of the Earth, with a 4000 mile radius), and it seemed to come up with 414.6 inches.

[Joff]

Assuming that you want a uniform height to the string: since you increase the circumference by 1 inch, you can increase the radius by 1/2pi inches. In real units that's 4mm.

Edit to add: On the pull-up to the horizon on an Earth-sized planet I got 413 inches (10.49m), close enough the same as hhEb09'1.

[Inferno]

With regards to the dots puzzle on page 1 ....

I drew a Z which is three lines, then a - through the middle for the 4th line. All the dots are now connected.