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Three glass puzzle

        

Three glass puzzle

Logo for Three glass puzzle
An old puzzle implemented in JavaScript. Several research question are asked about the puzzle, a couple of question are answered in a regorous manner. Two implementation are offered.
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Material Type: Simulation
Date Added to MERLOT: March 16, 1998
Date Modified in MERLOT: September 19, 2010
Author:
Send email to alexb@cut-the-knot.com
Submitter: Bethany Gross
Keywords: barycentric coordinates, math puzzle, graph theory

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About

Primary Audience: College General Ed
Mobile Compatibility: Not specified at this time
Language: English
Cost Involved: no
Source Code Available: yes
Accessibility Information Available: no
Creative Commons: unsure

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Discussion for Three glass puzzle

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Avatar for Katlyn McVeigh
6 years ago

Katlyn McVeigh (Student)

I spent a lot of time reading the material and trying out the water puzzle. It was really neat because it really helped me to understand the problem and helped me figure it out. This tool is great for anybody who learns better with pictures. It is a great teaching technique.

Avatar for gerilyn parente
6 years ago

gerilyn parente (Student)

I reviewed the materials for about an hour, I kept re-reading the material to try and understand it. So i tried to do the problem and follow it. It was still quite difficult for me to understand. If i had to evaluate the quality of the content i would agree that the material accurately present concepts and models that are eduacationally correct, because following the problem i come up with the same answer as well. The potential effectiveness for enhancing teaching and learning would be achevied if the teachers taught it well and explained correctly. Evaluating the ease of using the materials, for my first time was a little difficult to use the software, its a bit complicated. But overall an interesting experience and new way to check out math.

Avatar for derek velez
7 years ago

derek velez (Student)

this site reminded me of a problem with the igloos and power lines that we are currently doing in class right now. i felt like i could understand a little bit more now seeing as how we went over it during class today. overall i enjoyed the site and just like the igloo problem i am going to try and grasp the whole concept of the problem and see if i can figure something out i couldnt before
Time spent reviewing site: 20 min

Avatar for dorothy scott
7 years ago

dorothy scott (Student)

when i went to this sight i was very interested in the content that was there.I thought it was very informative and liked that there were also learning games as well as information about how to use this sight.
Time spent reviewing site: 20 minutes

Avatar for Natalie Cline
7 years ago

Natalie Cline (Student)

On this site I was able to explore several intresting topics which included; "Did you Know" intresting math facts, Coincidence/Proability, and "what is what". I found out how many people you need in order guess the probabilty of two people having the same birthday in a room. You need to check it out...you will find this under; "Did you Know". This is a great site if you have diffiuclty with math and like to to learn by having fun.
Time spent reviewing site: 1 hour

Avatar for Kris Mims
7 years ago

Kris Mims (Student)

A good website link.. Very imformative with the puzzle. I am not too bright when it comes to graph theory, however I followed this explanation better than I expected. I have mentioned this before, I believe websites with tons of information like these should be at everyones disposal.
Time spent reviewing site: 15 minutes

Avatar for Adrienne Reed
7 years ago

Adrienne Reed (Student)

I loved this site! I only wish that I'd know about it when my children were small. It is a great reference tools for parents, which will personally assist them to teach their children mathematics, or show them where to go to get help, or material. It is also beneficial for students who need help, as there is an interactive portion (CTK Exchange) that allows you to post questions, and receive responses from other members. There are interactive games, and puzzles that would keep a child, or an adult in constructive play for hours. I spent about an hour on this site, and because of the vast categories in math available on this site, I will use it as a tool if I have questions that my math buddy, or myself might not know the answer to.
Time spent reviewing site: I spent about an hour reviewing this site, and I do plan to return often this semester.

Avatar for Melvin Peralta
7 years ago

Melvin Peralta (Student)

Right when i first browsed through the site, i automatically spotted interactive examples regarding the related problems on the page. I viewed under the section of puzzles on graphs, "Lucky 7". I read through the problem about Lucky 7 and tried out the interactive example they had on the website, i failed miserably. The point was i was learning actively, this site provided alot of useful information about the puzzles that are solved through graph theory. For a first time user, i feel as though they'd really enjoy this site, for learning, or for using the example as a demo for their lecture. The site is at first technical in terms of finding more puzzles, but if the user thoroughly views the site page, the outline of links should catch there attention rather quickly.

Avatar for Mallory Walker
7 years ago

Mallory Walker (Student)

I Looked at this page for about ten minutes using the links provided and felt that this was a good source of information. I had never seen this material before and was able to learn much about it. I feel that the quality of this material was useful because it not only provided pictures and descriptive detail, but it also provided other links you could use to get more information. I felt that this was very effective because it used pictures to explain and other used other links to provide more detailed information. The materials for this page were easy to find and easy to understand by the descriptions. It also gave sub-headings for the other links related, so that everything would be easy for someone that had never used the site before. This was a very interesting topic and had a lot of information to help explain it.

Avatar for Brittany Rediger
7 years ago

Brittany Rediger (Student)

I found the Three Glass Puzzle interesting and graspable. I spent about 15 minutes poking around the website and reading. The highlighted words that have links to definitions and explanations were helpful with understanding the puzzle's steps. I strongly believe using puzzles in teaching truly enhances the interaction of a student or class, and this puzzle would do well in teaching applications of the graph theory.
Time spent reviewing site: 15 minutes

Avatar for Tom Secula
8 years ago

Tom Secula (Student)

It was very easy to use in the way of reading and understanding. I appreciate all of the people offering different solutions to problems.

Technical Remarks:

This material can be used effectively I believe for expanding the way students think about a single problem and where it can go. The content is high quality.
Time spent reviewing site: I probably spent too long trying to figure out the different puzzles and equations on the learning material. After 10 minutes of reading it all I played around with everything for quite awhile.

Avatar for Ruben Bravo
8 years ago

Ruben Bravo (Student)

It only took a couple minutes to go over the sites contents. It interested me because it seemed like a problem we would go over in my current math class. I tried out the problem and it took me a while to understand how to get it right. It's useful that all the possible solutions are shown. I also liked that it explains how to do each step. This site really relates to a math class like the one I'm in and is a good problem to learn about.

Avatar for Pavel Shokun
8 years ago

Pavel Shokun (Student)

I spent about 35 minutes reading the material on this site. Then I spent another 25 trying it. It has a lot of information and makes you put your brain to work. I made some of the materials way more complicated than it really was. I enjoyed working out the puzzles. The site covers many topics and provides solutions. The site provides great visualization of the subject, therefore making it interesting. It’s actually not as easy as it seems, to solve some of the puzzle. It is defiantly time consuming but fun. It helps a person develop critical thinking skills for sure. The materials presented are educationally significant but may seem hard to understand at first. The site contained graphics which was a great help. The material may seem a bit unclear because it seemed to me like it was lacking an introduction to the concepts. I would say that using this site as a teaching aid would not be the best way to go about teaching students on the matters described. It is an interesting tool for those who have a passion and great interest in math. Those who have the time and like math puzzles will defiantly enjoy this and probable could spend hours working on them.

Technical Remarks:

At first the site seems like it’s not to user friendly, but after some time anyone can defiantly get the hang of it. The puzzles are very interactive and interesting if you spend the time to work on them. The site can be improved to make it easier for users, because the concepts are were useful.

Avatar for Karambir Kaur
8 years ago

Karambir Kaur (Student)

It took me about 20 minutes to explore this website. It surely is a confusing website but after playing around with it for a long time I got a hang of it. I like this puzzle because it actually made me think about it and had me solve it. It is actually not as easy to solve as it seems. When you get in the depth of the puzzle you realize that it uses a lot of critical and conceptual thinking. This material definitely present accurate concepts and models that is educationally significant. As a teaching method the puzzle games are great exercise for all the students to use. It would be a little hard for the first time user to use this material because it takes a lot of exploring. But I think it is something that everyone can learn from and can get benefit from.
Used in course

Avatar for yonas workeneh
9 years ago

yonas workeneh (Student)

this site is great. i was confused at first but after spending a little more time i start getting the concept.it is fun has a lot good interactive information. at first i thought i would only spend a little time and i would get bored but i spent more time that i anticipated because it was fun and at times challenging.

Avatar for varun gandhi
9 years ago

varun gandhi (Student)

I spend about hour and half, I found this site is very useful, especially in it’s possible to develop one’s lateral thinking, as well as problem solving skills. I personally think that first time users, like I was one of them, will find it very easy to make use of this in future life. I’m sure I will use this site in my free time and also I have sent it is linked to my some friends to India. Anyone can benefit from using this site. Cool!!!!!!!!

Avatar for DucHanh Helen Bui
9 years ago

DucHanh Helen Bui (Student)

This is very interesting. I personally love this kind of puzzle games. I was able to figured out how to solve the 3 glass water game without reading the material after 10 minutes. The puzzle games are very interactive and great exercise for everyone to use.

Avatar for Justin Vincent
9 years ago

Justin Vincent (Student)

I had a lot of fun with this website. It helps with conceptual thinking. This website is very good for helping people who are struggling with visualization. As a teaching method this also makes the lessons a little more interactive and fun.

Technical Remarks:

You can spend hours going through all the different applications and problems. Its a great tool to get students interested in math.

Avatar for Errol Picazo
9 years ago

Errol Picazo (Student)

I spent about a whole hour looking through the material. The site does a great job at allowing students to look at different solutions on topics. I liked the puzzles and actually put my brain to work. When I first looked at the puzzle, it looked very easy. But never judge a book by it's cover. I had no luck in solving the puzzle, it led me in circles. The site has several tricky puzzles that makes a person think and try to solve the problem. Ideas and the graphics were very helpful throughout the site. In my observation, I feel that if it is used by other students it will allow them to use alot of critical thinking. The software was very user friendly along with the directions. Overall, it was fairly easy to use.

Avatar for   Gentry
13 years ago

Gentry (Student)

I spent about 15 minutes trying the puzzles. to me I felt that it was not
explained well enough to figure out the puzzles. The content of the software
talked about the history of the puzzle and how it was used.

Avatar for Jonathon Plambeck
13 years ago

Jonathon Plambeck (Student)

I spent about 10-15 minutes looking over the "Three Glass Puzzle" and I never
knew it could be so hard to understand math wise to pour liquid from one cup to
another. This article does help me understand it better and the graph helps a
lot.

Avatar for Aaron Loeb
13 years ago

Aaron Loeb (Student)

The time I spent was trying and reviewing the material from this link. From
this, I spent most of my time trying to figure out what to do on the site to try
to figure out the problems or issues discussed. Many of the problems I had
to read a few times to try to figure out what there was to do and how to solve
the problem. I was also interested to see what all the other links were on the
problems, as possible steps to help work through the problems.
I found the whole thing to be quit difficult. When I am on the internet
looking at a web like this, I feel like I am always looking for the fastest way
to find the answer to my question. When I am looking at something like Math, I
want to look at a book. I feel this site and problems had no introduction that
was clear.
I have taken other internet classes at San Jose State and I found those class
sites to be much easier to use. Everything was a step by step process making it
very clear. This site should be completely redone and make is more
user-friendly. At least I found it to be this way for The Three Puzzles.
Used in course

Avatar for Michael Woznicki
13 years ago

Michael Woznicki (Student)

I really enjoyed this puzzle because it was very visual. I learn alot better
when things are drawnout, so I was able to remain focused on the problem. I
found the program simple to use without conflict. This problem took me about
5mins to solve, and after I found the answer; I forgot how to solve it haha. I
liked the problem because it would show my previous steps, so i could learn form
my mistakes. So, I could visually see what I was doing wrong. rather then
trying to remmeber it on paper.
Used in course

Avatar for   belardes
13 years ago

belardes (Student)

i looked over this puzzle for a little while and i tried it out a couple times
and i found it rather confusing. Once i just stopped and thought about it for a
few moments i relized i needed to get one cup of water in a glass. so as soon as
i figured out what steps to take to get that i solved the problem. the second
time i tried the problem i solved it rather quickly.

i think this a good tool to use because many things in math are confusing at
first, but if you stay with it, you can learn it, and it feels better once you
know it.
Used in course

Avatar for Nhu Nguyen
13 years ago

Nhu Nguyen (Student)

I spent half an hour on this link because I found it interesting. I like
puzzles and find it helpful for my brain. It helps the brain become more
active and more sensitive to some tricky problems. The link has the content of
some tricky puzzles that force people to think. Some might be hard, some might
be not, but if we don't think hard, we cannot solve it. It also give out
different ways of solving the problems so that one can take a look for
reference. The explanation of the relations between numbers are also very
interesting and helpful to read. We can also get a general rules for some
similar problems. The software is very easy to use. I was the first
time user and I didn't have any problems using it at all.

Avatar for Erica Gonzales
13 years ago

Erica Gonzales (Student)

I spent about 30 min on this site. I only spent 30 min because I was stumped at
frist and I really wanted to figue it out. The question seemed familar to a
question my professor asked us in class about "the igloos." I got stumped and
frustraded and just I gave up. I just couldn't slove it. I enjoyed the site
though it was intresting and very creative. I'd use this in the class as a fun
thing to do and think about.

Technical Remarks:

I had a fairly easy time using this site.
Used in course

Avatar for Jason Piraro
13 years ago

Jason Piraro (Student)

i spent about 15 minuets trying to understand this but had a hard time doing so.
It is hard for me to be able and see the puzzle i need someone to tell it to
me. im not sure if this would en hance any learning.

Technical Remarks:

i think that first time users well have trouble with this because it is hard.
that is what i think about it.
Used in course

Avatar for Christopher Taylor
13 years ago

Christopher Taylor (Student)

I found this site to be particularly useful, especially in it's potential to
expand one's lateral thinking, as well as problem-related visualization, skills.
I spent well over an hour wrapping my brain around various problems, and the
explanations and analysis are top-notch. I think that first time users, as I was
one of them, will find it very easy to make use of the materials and they will
surely be pulled in by the many puzzles presented. I believe that this site
would be an excellent tool in helping students think "outside the box, " as it
were.
Used in course

Avatar for Charlene Byron
13 years ago

Charlene Byron (Student)

I spent 10-15 minutes reviewing the puzzles. I like the detailed description of the steps to solve. I thinks its great to also have member solutions published as well. For some people, like me, its difficult to visualize problems of this
nature. However, these puzzles are realistic enough to work on in a class or as
a personal
challenge. Pretty organized and user friendly!
<
Used in course

Avatar for Barbra Bied Sperling
13 years ago

Barbra Bied Sperling (Staff)

We spent 45 minutes doing one of the puzzle. The material was good but difficult
until we figured out we could not solve it. This was actually a good exercise
for us to think about. I took a group of three people to figure it out. It was
easy to use the software. When you click on link it takes you to the first
puzzle and you try it.
Used in course

Avatar for Tammy Vu
13 years ago

Tammy Vu (Student)

This is a good site to go to. The game was fun and interesting. It took me a
couple of tries but in the end i did do it. I was able to make at least one of
the glasses contain 4 oz. of water. The material presented here can be used in
an elementary school type of environment to teach kids on how to do math using
computers and making math fun. The model here allows for teachers to use this
as a teaching tool for students who find math hard and boring. This will make
math fun for the kids. This was very easy to use. The instructions were very
simple and thorough so that any one would be able to understand it. Even me, who
is so bad with instructions:)
Used in course

Avatar for Kathleen Dietrich
14 years ago

Kathleen Dietrich (Student)

I throughIy enjoyed this site. I spent 20 minutes checking out this site
of three glass cups. I was confused, at first, about the whole point of the game
because I have Math issues. However, after getting totally frusterated and
loosing paitiece (after about 15 minutes) I looked at the answer and it made
complete sense. I then enjoyed going back and doing it knowing that it could be
solved and that I could actually do it. Thanks for the brain exercise. It was
fun.

Avatar for Connye Paris
14 years ago

Connye Paris (Student)

I am a math g student and like puzzles. This is a good one! It is easy to
navigate within the software and keeps the user wanting to try again and keep at
it to solve the problem. The water puzzle reminded me of a scotch and water
puzzle our teacher presented to us in class - so I tried it out. Although I was
unsuccessful after trying three times, curiousity got the best of me and I
viewed how another had solved it. It poses to the user a very significant
problem solving technique - if at first you are unsuccessful, try it again with
a different approach or a different technique. I spent about an hour on this
puzzle.
<

Avatar for   Huynh
14 years ago

Huynh (Student)

I spent about fifteen minutes trying to complete this puzzle, unfortunately I
was unsuccessful at it. This puzzle does accurately present concepts and models
that are educationally significant because it helps show the users in trying to
come up with different models to try and slove the puzzle. By using this puzzle
in the classroom it will allow for a lot of critical thinking by the students.
The use of this software is very user friendly and the directions given are
very simple and can be understood by anybody.

Avatar for   greer
14 years ago

greer (Student)

i was planning on just viewing this for as short as possible, but because i
don't like being stumped, i have been here for a while.
i was surprised how educationally signifigant this was. there was a formula, or
equation, for every thing. that was very interesting to me.
i think so. with this web page a student can learn something like this at their
own pace. its a great tool to have.
i had a little difficulty at first, but i figured it out, and i am a computer
idiot. :)

Avatar for Dianna Pallack
14 years ago

Dianna Pallack (Student)

Thinking back to one of the Die Hard movies I saw, I remeber Bruce W. and Samuel
L. J. by a fountain and they had to undo a bomb. They had to measure 4 units
of water and they had a 3 and 5 unit container . The "3 glass problem" was
pretty much the same situation and since I forgot how they did it in the movie
after trying the problem for a little bit I was able to get the answer. I found
this site to be very interactive as well as educational and i would recommend it
to those who like math problems or just want their head teased with for a while

Avatar for   garcia
14 years ago

garcia (Student)

I spent a few minutes browsing this sight and I thought it was very interesting.
I think this sight is educationally signifigant because of it's content.
Possible solutions are given and each step is given and explained in great
detail. Because of this I think this sight is a great teaching tool and a great
educational tool. This sight was set up a little weird but was not hard to
figure out for sure. First timers should have no problem on this sight.

Avatar for Lupe Fuentes
14 years ago

Lupe Fuentes (Student)

I spent about 25 minutes trying to make sense of this puzzle and then solve it.
Not only could I not solve it, but I couldn't make sense of it. I found this
game pushing me to try over and over again, challanging me to solve it. I think
it would be interesting to see someone who knew what they were doing to solve
it and explain what they did to solve it. This game does present concepts that
are educationally significant, and I think by finding out how to solve this
would challange students to think critically. There was not a problem using the
materials and software.
<

Avatar for Jason Belligan
14 years ago

Jason Belligan (Student)

I spent about 25 minutes trying to solve the 3 glass puzzle. This is a very fun
interactive game it could be used as a in class project. Its challenging and you
have to try different combonations and keep track of what you did. I found it
very easy to use and try and try again. I finnaly did cheat and got the answer ,
and found the actual sequence of numbers fairlly simple.

Avatar for christine dominguez
14 years ago

christine dominguez (Student)

I SPENT A HALF HOUR ON THIS SITE "THE THREE GLASS PUZZLE". I READ ALL THE
PUZZLES,LOOKED OVER THE INSTRUCTIONS AND STEPS. I TRIED THE VERY FIRST PUZZLE
AND GOT A HEADACHE I USED THE TRIAL AND ERROR APPROACH BUT I GOT NO WHERE SOO I GAVE UP THEN
STARTED TO WRITE NOTES AND LOOK OVER THE STEPS AGAIN.I NEVER DID COMPLETE THE
PUZZLE BUT I DID STUDY THE SOLUTION FOR A WHILE. THIS MATERIAL DOES ACCURATLY
PRESENT CONCEPTS AND MODELS. IT GAVE GOOD INSTRUCTIONS THAT WERE PRETTY EASY AND
EASY TO UNDERSTAND. THEY GAVE NUMEROUS MODELS TO TRY,DEFINITIONS AND SOLUTIONS.
I THINK THIS WOULD BE A FUN EXERCISE FOR A MATH CLASS, IT WILL CHALLENGE
EVERYONES BRAIN TO THE FULLEST. I THINK TOGETHER AS A CLASS IF SOLVED IT WILL
ENHANCE EVERYONES BRAIN FOR A HOT MINUTE! AS A FIRST TIME USER I FOUND IT VERY
EASY TO USE. THE SOFTWARE IS VERY SPOKEN FOR...

Avatar for Sam Oshana
14 years ago

Sam Oshana (Student)

I spent another hour tonight browsing for more interesting articles on the
Merlot website, but instead I stumbled on the three glass puzzle at
(http://www.cut-the-knot.com/water2.html) which was very interesting since I
have been experiencing similar, but not so difficult puzzles to solve in my
current Math class. I liked the logic and reasoning that led to a possible
solution. I think more puzzles like this will be very helpful to stimulate a
student?s mind and inspire effective reasoning.
Sam

Avatar for   aboukhaled
15 years ago

aboukhaled (Student)

It took me 5 min to understand this puzzle, but it took me 45 min to solve--and
I never could. First when the problem drove me crazy, I was going to give up on
it, but then I asked one of my sisters to solve it, it challenged me to keep
going with the game. However, neither of us could solve, but at least we tried.
This puzzle is a very interesting game for your brain, because it makes your
brain work and think--even if u don't want to think. I'm not used to these
games, but I found it very challenging, especially when you play it with someone
else, and especially if that one is your sister or your brother, cause you want
to prove that you are smarter than him or her.
This puzzle was entertaining and challenging more than teaching, and a good
exercise for your brain.

Avatar for damian camarena
15 years ago

damian camarena (Student)

This puzzle had me for just about an hour. Although i was not able to solve the
problem I did enjoy trying. Everything was explained clearly and the graphs
were great but I just could not figure it out. At first I was just guessing and
hoping I could solvbe it that way but I was wrong. While opening up the
different pages to the problem I came across the step by step solution to the
problem which I thought was pretty cool. Overall i think this is a pretty cool
site if your in the mood to let your brain do a little exercise.

Avatar for Trimaine Eley
15 years ago

Trimaine Eley (Student)

I spent a total of twenty minutes, mainly because I was paying tweny cents per
minutes at the local Kinko's. I tried to solve the puzzle by trial and error. I
could not solve this puzzle by any means. This sort of problem, sort of reminded
me about the Igloo question, you asked towards the begining of the semester,
with the diffrent type variations. As a first time user, the software was very
understandable.

Avatar for   yount
15 years ago

yount (Student)

I spent 10 minutes trying to solve the problem and had no clue. I was really confused. I didn't understand it. I didn't see anything to help me out. The program would not help me learn. It was easy to use though.

Avatar for Dan Elrick
15 years ago

Dan Elrick (Faculty)

I love math when you are presented with a problem such as the three glasses
problem. I spent a good fifteen minutes figuring out the problem. I also tried
some other activities and they really make you think. This type of math is great
for teaching problem solving for everyday life. The material is pretty easy to
use and fun. Anyone can benefit from using this site.

Avatar for Kim Nguyen
15 years ago

Kim Nguyen (Student)

There's a lot of abstract thought involved which I liked because that relates to art and
creativity. I spent about 20-30 minutes reading through the site and trying out the different puzzles.
The theories seem interesting and the problems are challenging and would seem to be good material to present to students.
And the instructions seem basic enough to comprehend. A good site.

Avatar for John Garza
15 years ago

John Garza (Student)

I spent about 45 minutes trying to solve the puzzle. My first attempt was
trying to solve it by trial and error. No luck. I very quickly noticed that I
was going in circles. My second attempt was a better approach. I wrote down
all the possible variations of 8 and my list was rather long. As I was making
my list, I noticed why my trial and error approach led me in circles. I tried
to use another approach by trying to minimize my list which would utilize
certain combinations. Still no luck in solvivng the puzzle. I eventually
solved the puzzle but I was not sure on how I was able to accomplish it. After
I solved it, I looked at the answer and it made the puzzle much easier to
understand. When I first looked at the puzzle, it appeared that it was going to
be fairly easy to solve. I very quickly found out that it was easier said that
done. The three glass puzzle consumed by mind as I attempted to solve it. (My
original work was done on Friday 921 at around 10pm but I was unable to save my
comments.)
As a first time user, the software material was fairly easy to use.

Avatar for Deborah Swanson
15 years ago

Deborah Swanson (Student)

I browsed through the information that was provided and found that I could
easily understand what was being said. The site did an excellent job making it
less complicated for the students to learn the different solution methods. The
instructions were easy to follow and the quality of work was powerful.