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Logo for Cut-the-Knot!
This site is the parent site of an extensive collection of interactive mathematics authored by Alexander Bogomolny and includes an interactive monthly column . The content is accessible to the casual reader but offers much depth along with links to other high-quality resources. Altogether, this site is a mathematician's delight.
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Material Type: Collection
Technical Format: HTML/Text
Date Added to MERLOT: November 26, 2002
Date Modified in MERLOT: December 15, 2016
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Submitter: James Rutledge
Keywords: games, eye opener, chaos, Tower of Hanoi, visual illusions, logic, Pythagorean theorem, fallacies, geometry, proofs, arithmetic, combinatorics, puzzles, proofs of Pythagorean theorem, calculus, probability, fractals, algebra


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Primary Audience: High School, College General Ed
Mobile Compatibility: Not specified at this time
Technical Requirements: Java-enabled browser
Language: English
Cost Involved: no
Source Code Available: no
Accessibility Information Available: no
Creative Commons: unsure


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Discussion for Cut-the-Knot!

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Avatar for Sheila Morgan
12 years ago

Sheila Morgan (Student)

. How you reviewed the materials (Did you spend 5 minutes browsing, 2 hours
trying it, or actually use it in teaching-learning activities?).

I spent abbout 35 mins. reviewing the material on this site.

2. The quality of content (Does the materials accurately present concepts and
models that are educationally significant?)

I found information to informative and fun. The little applet above that said
did you know...? I foiund it to be interesting.

3. The potential effectiveness for enhancing teaching and learning (If used
appropriately, will students' learning and faculty's teaching be enhanced?)

I belive that for the most part people are visual/interactive before they are
analytical. It allows for a better understanding of concepts. Teachers will
find that the comprhending the principles if they something tangable that they
can apply it too.

4. The ease of using the materials (Will first time users find it easy to use
the software?)

I think that first time users will find it easy to navigate in this website

Used in course

Avatar for Cheryl Baker
2 years ago

Cheryl Baker (Faculty)

I find this great and plan on using some of the material in my course.

Time spent reviewing site: 1.5 Hours
Used in course

Avatar for Vanessa Wright
4 years ago

Vanessa Wright (Content Developer/Author)

This collection of material was very good. There were many interactive games that engage the memory, attention, and problem solving skills of learners. I inspected about 3 puzzles and one significant factor is that there was always an explanation that related to a real-world example. There were also many applications of various levels of math.

Time spent reviewing site: 25

Avatar for Selena Gutierrez
7 years ago

Selena Gutierrez (Student)

I spent 5 minutes browsing the website, and decided to play the Fish Soup game. The game was fun, and I assumed it had to deal with statistics, but there was no explanation on how the game was linked to mathematics. As a first time user, it was pretty easy to play, but seeing the direct connection to math and the explanation of what math the game was using was difficult.

Avatar for Josh Davies
7 years ago

Josh Davies (Student)

I spent fifteen to twenty minutes reviewing the games on the site. I found the site easy to use and a great way to understand concepts in another method of presenting the material (game). Im not a games person, so I would not go to the site for "fun". As a classroom tool, it may provide an alternative method of expressing more difficult concepts and ideas and a more user-friendly fashion.

Technical Remarks:

The site was easy to use, understand, and not difficult to navigate. A quick browse enables the student to see what is available very quickly.
Time spent reviewing site: Fifteen to 20 minutes.

Avatar for Rebecca Sarkissian
7 years ago

Rebecca Sarkissian (Student)

I took about ten minutes on this website and I loved it! I loved playing all the games, especially the easy arthimetic ones. The quality of the content was extremely informative and it was easy to use, and I believe for it to be very effective. As a student I feel like I learn best through games like this, it helps me to visually and mentally understand the concept!

Technical Remarks:

I love all the information introduced through a visual, interactive way
Time spent reviewing site: Ten mintues before I wrote this review, but I am going to play some more games after I write this because its so interesting!

Avatar for Jennifer Ly
7 years ago

Jennifer Ly (Student)

This site is a definite keeper. I spent about 10 minutes browsing. I liked the fun, engaging attitude of the problems, ranging from the most basic math to the higher level, here's-where-your-brain-gets-fuzzy math. material is given in an informative and clear manner for both teachers and students to use when they need it. It's simple, user friendly,arranged in clear organized categories, and makes math almost edible. Yes, edible. Students will benefit greatly from this site if they say, need a brush up on a concept or something.

Avatar for charlie sam
7 years ago

charlie sam (Student)

cut the knot has a lot of different mathematical subjects to choose from.Theres a verity of topics that can be used for high school and college students. The materials contain movies that you can look at if your more of a visual learner.The text in the material is interactive, making it hands on for the student.The site contains math games and puzzles making it more fun to learn. The site also chronology updates so you can find out more info so it's more useful. This site provides good info to any person that finds math difficult to learn.
Time spent reviewing site: 40 minutes reviewing the site and i found out a lot of wide verities of textual material that can be of help.

Avatar for Joseph Batto
7 years ago

Joseph Batto (Student)

the website has a variety of games and puzzles. Effective resource for high school/college students. Challenging. Good way to review various math problems.
Time spent reviewing site: I spent about 30 minutes browsing this site.

Avatar for Rose Marie Nario
7 years ago

Rose Marie Nario (Student)

Of all the link I have gone thru so far in Mathematics link, this Cut-the-Knot is one of web link that I will definitely will go back. It has very broad mathematical puzzles for all different mathematical subjects. I just tried the hour glass timing and was impressed on other people posting different solutions to the puzzle. Highly recommended to high school/college students.

Avatar for anthony blehblah
7 years ago

anthony blehblah (Student)

I find this website very fun, and filled with everything i would need and more.It was very easy, to find and use. It seems accurate, and on point. It would really help the effectiveness of a student or teacher.The materials were easy to follow and understand.First time users will find it very easy.

Technical Remarks:

I enjoyed this website.
Time spent reviewing site: 1 hour and 15 minutes.

Avatar for Angela Mullin
7 years ago

Angela Mullin (Student)

Vast amount of information including games, puzzles, tools to facilitate teaching mathematics and algebra. Lots of variety, interactive style. Students that thrive at math will enjoy the variety, students struggling with math concepts will either get overwhelmed or find the magic tool that suits their learing style.

Technical Remarks:

Easy to naviagate, the Did You Know? link was amusing.
Time spent reviewing site: 30 minutes

Avatar for Jacob Cook
7 years ago

Jacob Cook (Student)

can be great for geometry students or similar math. has a wide variety of tools used to learn such as puzzles and other games. different subjects and settings make this easily used and easy to navigate.

Technical Remarks:

this site could easily be used in a classroom due to its easy access to mathematical material and understanding and simplicity.
Time spent reviewing site: 5 minutes, easily could see the overall view of the page.

Avatar for brenda pinal
7 years ago

brenda pinal (Student)

good website to review maTH
Time spent reviewing site: 25MIN

Avatar for indra rungis
7 years ago

indra rungis (Student)

This site will be good for teachers and parents. it seems to be a good resourse for all your math doing.
Time spent reviewing site: 6 min

Avatar for Michelle Davis
7 years ago

Michelle Davis (Student)

So i was playing with a few puzzles and they are so confusing. To me i do not get some computer games or puzzles so this one was confusing a little bit. if i was showed how exactly to do this i think i could master it, but since i had to fend for myself i got lost. It is good for people that arnt like me, because im a visual learner and hands on.

Avatar for Nabeel Oqbi
8 years ago

Nabeel Oqbi (Student)

I spent about 30 min playing in the puzzle, The most important thing about this site that I have found a solution for the 3 Utilities Puzzle that my teacher gave in class.
Time spent reviewing site: 30 min
Used in course

Avatar for Dr. Troy Tenhet
8 years ago

Dr. Troy Tenhet (Teacher (K-12))

I like it...I think. I need to figure out what to do with the site now...

Avatar for Pavel Shokun
8 years ago

Pavel Shokun (Student)

I spent about 40 minutes browsing and looking at all the interesting sites. I spent some time trying out some of the games. I ran into many interesting quotes and some of the games were actually really fun. The site is very user friendly and only several of the links did not work properly. The games are very educational. The games I looked at covered materials such as probability, algebra, geometry, arithmetic’s and more. It’s a very useful and informative site. It’s great that it has so many games and interactive activities to choose form. All of the material presented on this site is educationally significant. I would recommend this site to students, parent and teachers. It provides lots of information and help with all types of math problems. Children can use this as a site they can play on and also get help with math. Teachers can also use it to demonstrate concepts and make it interesting for kids. It explains math concepts in a non boring form. This is a great site and its very educational. It’s a great site to go to just have some fun with math. There is some material that I found rather challenging but I like challenges, this is a site I will defiantly come back to in my spare time.

Technical Remarks:

The site is simple to navigate around, and it’s well organized. It’s very knowledgeable and defiantly helpful. It does not have too many flaws or problems. It’s a great resource for those who don’t really like math but like games because they will learn math. The site is suitable for users of all ages. I will use this site in the future and will tell my friends about it.
Used in course

Avatar for Rajbir Kaur
8 years ago

Rajbir Kaur (Student)

I spent about 30 min. playing the games on this site. They were enjoyable even though i had hard time to figure out the solution. The material accurately present concepts and model that is educationally significant. I think the material can helpful for anyone who is searching but it’s little hard to understand and also little challenging.
Used in course

Avatar for Asim Pasha
9 years ago

Asim Pasha (Student)

So far it’s been about 15 minutes and it’s a bit of an odd yet interesting site. There are many interesting puzzles to be played which involves math (obviously). It has many references other types of math including Probability, Geometry, and algebra. At first glace it seems a bit intimidating, with so much information just right there in your face. It just seems a bit uneasy, because you don’t really know where to start. However it is a very informative and I say it’s a good place for a novice student to read up on.

Avatar for Rosie Berdejo
9 years ago

Rosie Berdejo (Student)

I spent about 40-55 minutes reviewing this site. I found very interesting and educational information for example "veen diagrams are used widely to bolster thought process in every walk of life, whenever decisions have to be made. Venn diagrams are helpful in solving puzzles, and also for validation and derivation of syllogims". I'm sure instructors and students can enjoy and use this site as a tool. It has problems about Arithmetic, Algebra,Geometry, Math Games and Puzzles. This can help people who don't like math.

Technical Remarks:

I think this site is well organized and easy to navigate. I would use this site in the future.

Avatar for manvigas singh
9 years ago

manvigas singh (Student)

this website is great. it has a lot differnt types of problems that you can view. it has problems about Arithmetic,Algebra,Geometry,Math Games & Puzzles and etc. i recommend this website because it shows you have to do some hard problems.

Avatar for DucHanh Helen Bui
9 years ago

DucHanh Helen Bui (Student)

This is a great website. Very informative and interactive. I spent more than an hour reading on the games. I would absolutely recommend other people to visit this website and learn the games'material. The site is very user friendly and the language is very easy to understand.

Avatar for Errol Picazo
9 years ago

Errol Picazo (Student)

After the many sites that I went through, this was the best site that I have entered so far. I spent about 45 minutes browsing through the site. I think the Interactive Mathematics and Puzzles were useful. I thought this page is very useful in trying to solve math problems using interactive games. The site has a very simple and has effective design that navigates you around. As a student, it provided a collection of interactive applets which allowed you to voice out your opinion in an open forum with other people. I thought this site had all sorts of math games which either were easy or hard. If you could not solve the problem it allowed you reset it and try again. It showed tips and examples of several problems. Also, it allowed a better understanding of the concepts. It has many tools and many explanations of math theories that are very informative. I believe that this site can apply a great deal of understanding concepts both visually and interactively. Overall, this site was a great site to pass through. I give this site a two thumbs up!

Technical Remarks:

Students will find this site very useful and knowledgeable. I think this site is suitable for different users besides students. It was easy to navigate around the site with no problems.

Avatar for Robert Falk
10 years ago

Robert Falk (Student)

This is an exciting site of interactive Math games and puzzles, covering numerous topics such as Algebra, Geometry, Fractions, Probability, Etc.

Avatar for Natalie Bell
10 years ago

Natalie Bell (Faculty)

I find this page to be a source for students as well as teachers and parents to
go to. It provides a lot of help for the students in a variety of math classes.
For the parents it can help them find ways to help their children with their
assignments. Then the teachers can use this in their lesson plans and use it in
the classroom for extra help for students. Overall this is a good website & it
has games to help learn the material as well as explaining math problems
virtually instead of just the plain paper and pencil way that most people learn
math. =)

Technical Remarks:

I had no technical problems. It also has what will be used for the thing that
is wanted to be looked at. (ex. Three Roads, Three Travelers [Java])

Avatar for Liese Piggott
12 years ago

Liese Piggott (Student)

This is a very user-friendly site full of interesting quotes, interactive games
and information. I spent about 30 minutes on the site and tested various links,
including the interactive games which I found very interesting and
educational... I have no specific favorites but recommend others give it a try,
even if just to keep the mind stimulated. The site also sprinkles a lot of
interesting quotes throughout the different pages and all the mathematical
statements and theorems I came across were very easy to understand. This is a
site I'm sure instructors/professors and students alike can enjoy and use as a
Used in course

Avatar for R Ruiz
12 years ago

R Ruiz (Student)

Some of the comparisons that were made (between the math concepts and examples)
were rather poor and quite confusing. As far as content- the basic information
was all there and could be rather helpful in reviewing the topic of

Technical Remarks:

The pop up images which one could manipulate made the site fun to understand
Used in course

Avatar for concepcion guitron
12 years ago

concepcion guitron (Student)

I spent about 30 minutes browsing and working on the activities and by the time
I logged off I was absolutely lost. There was a series of interactive
mathematics miscellany and puzzles. I tired to word out a couple of the puzzles,
but they were too confusing for me. This site a site also provides several of
information about different puzzles, for example about geometry, probability and
other mathematical material. I think this site had a bit to much information,
as I was browsing and trying out the activities I felt overwhelm. I think the
material can be helpful if uses for research, with the expectation that the
material is hard to understand. This material appears to be challenging to
Used in course

Avatar for Ryan Hendry
12 years ago

Ryan Hendry (Student)

I spent about 15 minutes looking over the material for cut the knot. I saw a lot
of mathematical games that I thought were interesting and they sort of helped
me to understand what I was doing a little better.

The content seemed a little unorganized and I sort of got a little lost when I
first started to look at things, but I finally found my way around and it all
worked out fine.

This could definatly be a good teaching tool, especially for those people who
learn with hands on types of things. I liked the use of ganms to help explain
mathematical techniqes. It really help me out.

Some of the materials were kind of tricky and it took me a little bit to figure
them out. I just had to read the directions carfully and make sure that I was
doing evrything right. All in all this website was very interesting.
Used in course

Avatar for   Furia
13 years ago

Furia (Student)

I thought that this site was quite interesting. I enjoyed going through serveral
of the games. They were enjoyable even though i was unable ever beat the
computer or figure out the solution. I tried the 3 glass game, the night game,
the 7 coins, the date game and the bogus nim game. All of which i lost but i
found very thought prevoking. I feel that these games could be brought in to a
school envirernment and be found to be very beneficial to a classroom were
students would be forced to really utilize their minds and try to solve these
problems. I found that this site was very user friendly and made it quite easy
to navigate.
Used in course

Avatar for   Gentry
13 years ago

Gentry (Student)

i probably spent about 20 minutes on this software. I played a few of the games.
The games had an explanation link to them if you needed help. The information
in the material gave good explanations.

Avatar for Jonathon Plambeck
13 years ago

Jonathon Plambeck (Student)

I spent about 15-20 minutes looking over the site. The explains well about a
person who doesn't like math for a particular reason. This site can help people
who hate math for one reason or another. Its a more hands on expirence.
Better than just reading something in a book. When it is put in an interactive
format you can work with your hands. If something is wrong it will tell you.
Not make fun of you, not critisize you, or anything of that sort. Very good

Avatar for Dawn Minami
13 years ago

Dawn Minami (Student)

I spent about 25 min. reviewing the site. By reading the manifesto I got a feel
for the flavor of the site - that is, the site covers a lot of mathematical
material that you may have wondered about and gives quite a few ideas and
answers that the average person would never think about. I liked the 'Did you
know that...' section because it offers a recreational view of math that is
beneficial to the 'math phobic' The site is well set up and easy to navigate.
I would use the site in the future.

Avatar for Ross MacDonald
13 years ago

Ross MacDonald (Student)

I spent a good bit of time on this site, of course p[laying the games. They
were an interesting way to present math theories, but I think a less complex
explaination of the solution is needed. And I am not sure exactly what the
Memory Game has to do with math, as there was no explaination. All together, a
very good site, with many tools, many explainations of math theories.

Avatar for   Haman
13 years ago

Haman (Student)

I did not speed a ton of time reviewing this cite, but in the time I spent the
cite seem like an endless source of mathematical information. It had everything
from an extensive glossary to a interactive activites to proofs. This could be a
good tool for teacher to put to use.
Used in course

Avatar for   Pacheco
14 years ago

Pacheco (Student)

I am not a math person and this was really fun. It was nice doing math in an
interactive game mode. You don't want to drift off on this math. I really paid
attention. Some problems were challenging and some were extremely hard.
Overall the hour I spent didn't seem like a math class.

Avatar for   dixon
14 years ago

dixon (Student)

Wow!!!! That was the best web page. I think "Interactive Mathematics Miscellany
and Puzzles" is very usefull and user friendly. You can spend many hours and not
be bored of math. Yes that is a true statement. I thought that the page is very
useful in trying to solve math useing interactive games. I play video games
that can rot my brain, but if I spent not play video games and started
"Cut-the-Knot" web page I would learn more about solving problems. I thought
this page had all sorts of math easy and very hard games. The cool thing is that
if you can't solve you can reset and try it again. Also it show tip and example
of problems.

Technical Remarks:

Very user friendly......WOW!!!!!!!!!
Used in course