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Abraham Lincoln Quotes, Easter Eggs
Monday, June 25, 2007
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Easter Eggs
I decided to add an Easter Egg Hunt to The Problem Site. This is just a few odd pages scattered throughout the site that either have a joke, an interesting picture, an odd piece of trivia, or hints for solving puzzles on the site.
Hope you have fun looking for those!
Absence From Quote Puzzler
Probably some of you have noticed that I haven't been doing the puzzles on Quote Puzzler lately. The reason for that is very simple.
Periodically I have to go into the site and set up a new batch of quotes for the coming months. And, of course, when I'm setting them up, I have to look at them, which means I run the risk of remembering them. So, when I set up new quotes, I usually stay away from the puzzles for a week or two.
This time, as I was setting up the puzzles, I found some interesting quotes by Abraham Lincoln which were far too long to use as puzzles, so I thought I'd post them here for your consideration:
Quotes By Abraham Lincoln
Let me not be understood as saying that there are no bad laws, nor that grievances may not arise for the redress of which no legal provisions have been made. I mean to say no such thing. But I do mean to say that although bad laws, if they exist, should be repealed as soon as possible, still, while they continue in force, for the sake of example they should be religiously observed.
Discourage litigation. Persuade your neighbors to compromise whenever you can. As a peacemaker the lawyer has superior opportunity of being a good man. There will still be business enough.
I am a firm believer in the people. If given the truth, they can be depended upon to meet any national crises. The great point is to bring them the real facts.
On a related subject (not related to Abraham Lincoln, but to my absence from the site), for the next six weeks I will be away teaching at various camps around the state, so I will be on the puzzler sites very little. I will still check in from time to time, but if you have questions or issues with any of the sites, your best bet is to email me: dtwitchell@virtu-software.com. Be sure to specify which site your question pertains to, and give as much detail as possible.
I hope everyone has a GREAT SUMMER!Labels: easter eggs, quote-puzzler, theproblemsite
posted by Douglas Twitchell at
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Tough Puzzle, More Geometry
Monday, June 18, 2007
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A Tough Puzzle
Last week some of the people at Tile Puzzler started playing around with some more complex "Free Style" puzzles. Puzzles involving shapes with six square units, seven square units, etc. Some of these have been really interesting. karill created a puzzle titled NineNineNine, which consisted of a square (nine by nine, of course) which was created with nine pieces, and each of those pieces had an area of nine square units.
That puzzle stayed in the unsolved list for ALMOST an entire week (which is practically unheard of!)
Give it a try, if you want a bit of a challenge!
NineNineNine
Some More Entrapment Geometry
Entrapment continues to be a popular game at The Problem Site.
I've added in a feature to track how much time you took, and the average time for each puzzle. This way you can compare how you did with how everyone else did.
I wanted to show you another Entrapment puzzle. Take a look at this screen shot:
This might look a bit intimidating, but remember, we start by looking for triangles. In this case, we can find three similar triangles. Did you find them?
The next thing you might notice is that one of the triangles is in reverse orientation. You see that? Guess what! This is the triangle that you should start with. Can you entrap that triangle?
ANd with only two dots left, can you entrap the rest of the computer's dots? You bet you can!
What was the point of that little exercise? Not much - just to point out, again, that the Entrapment puzzles are most easily solved by focusing on triangles!
By the way, when I solve the Challenge puzzles, generally it takes me somewhere between twenty seconds and a minute, although once in awhile I get one that takes me five or six minutes to solve! What about you? How long does it take you to solve an Entrapment puzzle?Labels: entrapment, tile-puzzler
posted by Douglas Twitchell at
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A New Look!
Saturday, June 9, 2007
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I thought Entrapment was going to be my last modification to the Puzzler Sites before beginning my summer of camp work.
I was wrong. As I was thinking about the various puzzle sites I maintain, I realized that all of them had very similar layouts, with one glaring exception: The Problem Site. This was one of my very first websites ever built, and its layout was vastly different from all the other puzzle sites.
As I thought about this, I decided I wanted to make The Problem Site similar in layout to the other puzzle sites, but still maintain some of what made it distinctively different from the others. Accordingly, the new layout has a similar menu system, similar borders and backgrounds, but still maintains the right-hand sidebar, which regular visitors to the site will recognize as a distinctly "TPS" feature.
Along the way, I added some new features, like some more attractive buttons:
 
And there's a fun new navigation system at the bottom of each page. On every page you'll see icons that looks like this:
Every time you load a new page, the icons at the bottom will change, so you'll always have some fresh new feature of the site to try out. And, for the adventurous, there is the "Surprise Me!" button which you can click to be transported to a randomly selected game.
Obviously, with all the changes made all at once, there is a risk of introducing some "bugs" on the site. So if you have any problems, please use the site's contact form to let me know, or post a comment here!
Thanks,
DougLabels: theproblemsite
posted by Douglas Twitchell at
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Geometry Of Midpoints
Tuesday, June 5, 2007
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Last week a new puzzle titled Entrapment was posted on The Problem Site. This new puzzle has already become a big hit on the site, more than I anticipated. Within just a few days there were already close to 2000 puzzle solutions submitted.
On the puzzle page I gave the following hint:
Start out by trying some of the "Practice" puzzles. These are all puzzles which contain exactly three red and three gray dots. What you will discover is that most puzzle solutions are built around triangles, so if you can master the easy puzzles, the more challenging puzzles can be broken down into smaller, more manageable pieces.
I thought I would elaborate on that just a little bit, because the Geometry of the Entrapment Puzzle is quite interesting. The Geometry of Entrapment is the Geometry of Midpoints, and of Triangles.
Take a look at the following image, which shows three completed "Practice" puzzles:
What do you notice about each of these solutions? First, you should notice that the three red dots form a triangle (of course! Three points in a plane always determine a triangle!). Second, of course, the gray dots form a triangle as well. What should also be apparent is that the gray triangle is similar to the the red triangle. And when I say "similar", I'm using the geometric definition of the word similar. These two triangles have congruent angles, and equal ratios of sides.
In fact, if you think about it for a moment, you'll be able to figure out what that ratio of sides is. Are you thinking about it? If you're not sure, you can scroll down to the bottom of this post, where you'll find the answer.
Now, the other thing which is interesting and helpful is the fact that if you pick any two red dots and draw a segment connecting them, there will be two gray dots that define a segment parallel to that segment. Take a look at the picture if you don't believe me. Remember that from your Geometry class?
All of a sudden you should realize why the "Practice" puzzles are called "Practice" puzzles - once you understand the Geometry of the situation, there is very little Problem Solving involved; you can solve each one of the Practice puzzles by counting distances and creating parallel segments.
So why bother with the Practice puzzles? Because if you can get the hang of entrapping triangles, the other puzzles get much easier. Take a look at this puzzle:
A puzzle like this can look very intimidating - and some are even more intimidating than this. But if you can quickly locate triangles to entrap, the puzzle gets easier. Here's an example:
It took me only moments to recognize that triangle which could be entrapped. Note the similar triangle, the common ratio, and the parallel sides. From there I would start placing other dots to maximize the number of red dots entrapped. But it all starts with finding a triangle you can entrap.
When I first started solving these puzzles, I thought This is insane - these beastly things are unsolveable! In reality, even the most challenging Entrapment puzzles can be solved within a minute or two, if you can find the correct triangle to start with!
Have fun ENTRAPPING!
Ratio of Sides: Well? What is the ratio of sides? Did you say 2:1? If you did, you are correct. I won't take the time to do a proof here, but it's well known that a segment connecting midpoints of two sides of a triangle has half the length of the third side.Labels: entrapment, geometry, theproblemsite
posted by Douglas Twitchell at
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