10 January, 2009

The greatest math problem ever

This is a problem, which can be easily solved by children before entering elementary school. If you want to give it a try, please forget everything you have ever studied. Here it comes:

8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0

2581 = ?

I took it from here (Russian)

82 comments:

Daniel Lemire said...

My wife, who never studied college mathematics, found it easily (count the number of closed loops).

I could not figure it out. I have a Ph.D. in Math.

Lemeshko said...

I hope to earn PhD in physics in 2 years or so, but there was absolutely no way for me to solve this problem.

Lemeshko said...

By the way, let me guess... Probably what you call "counting closed loops" is called "counting zeros" by your wife? :-)

Sui Fai John Mak said...

The answer is 2.
Here is the reason:
The number of 2 is the 21 number
If you subtract the 7th number (2) by 6th number (0)= 2
If you subtract the 14th number (5) by 13th number (3) = 2
If you subtract the 21st number (x)by 20th number (0), it should give you 2
I don’t have a PhD yet. But I am passionate in Mathematics, and is interested in Game Theory in my Operational Research studies in my MSc.
It still took me 5 minutes in working it out. I could see why it is difficult. Simply because people would like to share the problem, but how about the solution? That is outside the square!
You are welcome to visit my blog
http://suifaijohnmak.wordpress.com
I could make up these type of mathematical problems if you like.
My email: suifaijohnmak@yahoo.com.au

Lemeshko said...

Sui Fai John Mak, thanks for your comment.

Unfortunately, it looks as I haven't get it. If you subtract 6th number from the 7th one you obtain 7662-3213=4449...

Can you describe the method once again please?

P.S. Why don't count zeros?

Sui Fai John Mak said...

This is a method based on a difference in a series: i.e. the difference between consecutive 6th and 7th and then 13th and 14th and then 20th and 21st numbers etc.
At first glance, I couldn't find any relationship between the sum of the the numbers and the number sequence. My deduction is then that there may be a series of "pattern" that repeat its sequence - i.e. either the sum or difference of 2 consecutive number in the "series", where there is no pattern in the first five, but repeated difference in the 6th and 7th number etc. This is similar to the nine dot experiement, where you need to join nine dots with 4 connected straight lines without leaving the paper, with the end of one line joining the start. Have you tried that before?
Concept is think beyond the square.
I am not sure whether this is challenging or not, but I really appreciate you directing me to this.
Hope you have every success in your PhD study. Great to meet you here.
John

Lemeshko said...

Thanks, John...

Sui Fai John Mak said...

I think David has got the correct explanation in Daniel's blog. I have also included David's answer on my blog to avoid any confusion.
Interesting to note that by comparing numbers could reveal something. I reckon this is not easily tackled by elementary school students. However, the logic behind could cause some uncomfortable feelings with children, especially if they don't see the "logic". This is something like computer logic based on a conversion system of a number to a binary digit system etc. I have left some comments in my blog as reflection.
Great to be "challenged" and re-think about learning after this experience. I may be the first to give reasons as I mentioned in my comment, though the reasons are not correct, in retrospect. It really makes me think of learning in the blogosphere, where the same situation may happen.

Sui Fai John Mak said...

When I first saw the problem, I did see the pattern of those 0 derived from a set of same numbers. I speculated that there was an operation or conversion in the set of numbers. However, I didn't think it matters much as it seems any equation could be operated like that. May be that is often due to our mind set based on education - rationality and logic. It really doesn't work here.
However, if kids have been trained to have such mind set once in their lesson, it is easy for them to transfer the learning to other similar problems. So, one experience in "intuition" may help in unlocking some of the toughest math problem.
I also noted that some of the IQ tests are not reliable measure, as one could improve the IQ score through repeated drills. I have tried the IQ test when I was young, and have since realised that one could improve upon repeated practice. I think IQ test could improve one's patterning skills.
I think the "aha" moment coming out of the learning are equally important in establishing one's confidence in tackling similar life problems. So, I think you collection of this problem is already a smart move.

Eugene Volokh said...

Nice problem; linked to it. But isn't the original in Byelorussian, rather than Russian? (I'm pretty sure it's not in Russian, though it's intelligible by Russian speakers, plus it's on a .BY domain.)

Lemeshko said...

Dear Eugene, thanks for your comment.

No, it is Russian. :-) Actually, in White Russia (or Belorussia), Russian is more widely spoken than Belorussian nowadays.

You can compare wiki articles about Belorussia, written in Belorussian

http://be.wikipedia.org/wiki/Беларусь

and in Russian

http://ru.wikipedia.org/wiki/Белоруссия

As you can see, in Russian there are no such letters as "i" or "ў" for instance. The former one is absent in the Ukranian as well...

Lemeshko said...

Sorry for the misprint, the "ў" letter is absent in the Ukranian, while "i" is present.

Eugene Volokh said...

Very sorry -- I stand corrected, thanks!

Anonymous said...

My wife (Master in mathematics) and I (Lowly MBA) spent all day thinking about this problem and could not solve it - quite frankly we were a bit embarrassed by the answer... but also appreciated the beauty of its simplicity.

Thnx for posting

Cantay said...

So, uh, I minored in math and can't make heads or tails of Sui's solution, and the Daniel's closed loops thing really throws me.

But yeah, I came up with 2 too. I just noticed that if you let all the numbers on the left side of the equals sign be symbols instead of numbers (e.g. saying that "0" is worth 1 since "0000" is equal to 4). Doing that you find that all primes are worth 0, "1" is worth 0, "8" is worth 2, and all other numbers are worth 1. So 2581 is 0 + 0 + 2 + 0 = 2. I mean, this sort of solution is consistent with all given left-hand sequences and it seems like something a child could do.

Lemeshko said...

Thanks for your comment, Cantay. This is true, one can "map" 0 to 1, 8 to 2, 9 to 1 and so on. This was proposed by David, in 11th comment to the Daniel's post:

http://www.daniel-lemire.com/blog/archives/2009/01/10/finish-this-sequence-of-equalities/#comments

Another issue is that you should forget about math, and consider numbers as unknown symbols.

Best,
Misha

enigmania said...

Hmm, I have a math/physics bachelors and a physics phd and I figured it out in under a minute. Your comment that preschool children could figure it out was a pretty big clue that it would be graphical rather than textual cues. It took a bit of mental squinting to stop reading things as numbers...

mmmm said...

2

Zachary said...

Does it really count as a math problem if it's just a pattern among shapes?
This is certainly a clever logic problem, but I don't think this would play as a math problem.
(but then again I'm a physicist not a mathematician, maybe the logic and math are one in the same at some level.)

Lemeshko said...

Dear Zachary,

This is a math problem, since topology is also a king of math :-)

Misha

Anonymous said...

Zachary... if Mathematics is something it is the science of PATTERNS, so this is indeed a math problem :)

Cross_blade said...

In my opinion, it's 2 because you have to count te circles in the numbers.

0000=4
7777=0
...
2581=2

Sorry for my bad English, I'm from Argentina. :)

Cross_blade said...

But te way is exellent.

agelstavr said...

The answer is: 2581=2.
It counts the circles each four-digit number has. Maby if it didn't start with "it can be easily solved by preschool children" and "forget what you' ve learned", I wouldn't have figure it out.

Anonymous said...

Sui Fai John....

Could you please stop being ridiculous??

C'mon closed circles and that's it.

guille roccuzzo said...

guille roccuzzo
its very simple the code has given in the examples, if you see the add of 1,2,3,4,5,7 is 0, so they don´t have value, but the add of 9 is 4 so its value is 1 each one of them, the 6 and the 0 is the same, and the 8 is 2, because of the first example given, which is 8809=6, the eights add 4, the 0 one, and one the nine, ist six when you add it all, an the last which is 2581=2 because the only number which have value its 8, and is it 2, if you dont get its for my explanation because my inglish its very bad, well i'd never been good in mathematics, but this took me five min to resolve it, I'm proud of that, jaja, at least I'm like six years old kid, jaja

Lemeshko said...

Dear Guille, that's a good guess...

Anibal said...

So interesting. I don´t know what is the answer......... i am going to think.

Actualidad Real Madrid

Anonymous said...

you can say all that... but if you look at the key and just add you get the correct answer...

0-1
1-0
2-0
3-0
5-0
6-1
7-0
9-1

by the first sequence of numbers we know 8-2

so 2581- 0+0+2+0

Anti said...

It's tricky because it's mislabelled. It has nothing to do with "Math" in the sense we're thinking when we read "Math Problem".

The solution isn't in mathematics, it's in the ability to recognize a pattern in images that, in this case, just happen to be numbers.

That being said, it's fun and I plan on driving my friends batty with it.

:)

Alejandro said...

It's pretty funny how people here think about the map

0-->1
4-->1
6-->1
8-->2
9-->1
elsewhere -->0

to solve the problem. Actually, this mapping count the number of circles (or closed spaces) into the numbers, so it's the same answer of counting circles.

Anonymous said...

It made me feel very stupid, after reading that you just count the number of closed loops. ^^;

Robert Benea said...

Pretty cool problem, I added to project eureka (hope you don't mind).

http://projecteureka.org/

If you want to solve other interesting problems, I advise you to check it out.

Anonymous said...

I graduated in mathematics and teach mathemathics for a living.
It took me 3 seconds to get it, really.

It's 3am in Italy now, and I feel good :)

(sorry for the anonymous post - my name is Giuseppe and here is my mini-site: http://sigurd.altervista.org/)

sav said...

I'm a computer programmer and I caught it immediately. Learn to use both sides of your brain.

bwolper said...

Got it!! If I hadn't seen the "closed loop" hint, I would never have figured it out. Thanks!

Dave said...

This was fun. Thanks. You are right, if you forget all concepts of math the answer was simple. It was interesting to listen to my thinking as I was trying to forget what I know. Thankfully, though, I have young grandchildren and imagined how they would solve the problem.

cory said...

what a waste of time, i think people are easily distracted,and make-up things to pass the time but this is just plain stupid

Shawnotron said...

I got the answer by finding a new value for each number.

1=0
2=0
3=0
4=N/A
5=0
6=1
7=0
8=2
9=1
0=1

I did this with basic algebra, but I guess all I had to do was count closed loops. Although, my math did count the loops for me.

Jeremy said...

That was amusing. I probably wouldn't have gotten it if not for the hint that it "can be easily solved by children before entering elementary school", which made me realize that the actual meaning of any of the numerals probably wasn't important.

Lemeshko said...

2Robert,

You have a pretty cool problem set on your website. Thanks for adding this puzzle there!

Abel said...

I agree with those saying it is mathematics - it's not what you traditionally think of when you think "math", but just reading the comments, some people used a mapping, while others used topology. The fact that it uses our symbols for numbers doesn't make it "not math", instead it seems like it was designed to throw people for a loop.

Jean L.N. said...

If it is (n0t) Math, then what is this:

ABBC=4
APPO=3
FFFF=0
fghi=1
gdpi=3
QPRS=3
klmo=1
GJWS=0
dcpr=2
COOL=2

bBQ4=?

Lemeshko said...

2Jean

The result is 4 or 5 actually, depending whether you consider "4" as having a closed loop. You should have included this number in your sequence, in order to make it clear...

Since you do not count the loop in the "A" letter, the answer is 4, I suppose.

Jean L.N. said...

Lemeshko,

You are almost right, there is more to it.

But you've brought a good solution: the answer could be 2-fold indeed.
Would need an extra chair then!

Martha said...

COUNT THE HOLES IN THE NUMBERS

9=1
8=2
7=0
1=0
0 has one hole, so 0=1

SO THE ANSWER IS 2
2!
2!

Anonymous said...

I'm an X and nobody cares, but I got it in 1.2 seconds, before I even read the answer. I'm telling everyone on here because I enjoy other people thinking my e-peen is large!

Chuck said...

Not too hard if you pay attention to the hints. I figured it out in less than a minute. I have to worry about some of you though. What kids start school with knowledge of primes?

Kaye said...

I also have a PhD in mathematics. I worked out that we were assigning different values to the numerals and summing them. I didn't get that it corresponded to the number of loops.

Anonymous said...

The real hint was that children could solve this easily BEFORE elementary school. So, no concept of even basic mathematical operations. Meaning you should have just looked at them as figures and not numbers. (I teach high school Geometry by the way, so figures are my life!)

Anonymous said...

If pre-elementary schoolers can figure it out then there is no computations involved. Therefore you should look at the representation of the number rather than what it represents. I am a Senior in college about to do my student teaching for teaching high school mathematics. Lets just say it takes a crazy person like me to look at it non-mathematically.

Jasmine said...

it is soo easy
e.g: all the numbers that have 1,2,3,5,7 in them are equal to 0 like 3213=0
based on this you can figure out other ones, 9=1, 6=1, 8=2
so 2581=2
(i've just finished high school tho, no higher education yet)

Lemeshko said...

Dear Jasmine,

Please get back to this problem after earning a PhD in math :-)

Jasmine said...

Dear Lemeshko,
you said "it can be easily solved by children before entering elementary school" so i think im much older than that :)
and i believe i got it right, it's 2...

ktkutthroat said...

Oh my god, just count the circles within the numbers.
Some of you people have WAY too much time on your hands.
The answer is 2.
~KT

suifaijohnmak said...

Misha, I think you have got the magic wand that has turned this exercise into an interesting discussion. Looking into the loops could only give us the "exact" solution, but looking beyond the discussion and interaction would inspire us to analyse problems in the world with different perspectives, realising that there are many problems that may have multiple solutions, though some may explain better than the others. So, by just presenting with a problem - like this, you could inspire people to THINK. Would a Maths teacher be able to generate such an interest in discussion, by posting a school problem? This is wonderful. Congratulations.

Anonymous said...

I got it after the first two numbers in the sequence. My IQ is >140 and I have never studied college mathematics.

Anonymous said...

For all those that said they were PhD students or masters students or whatever in mathematics, I claim the answer might as well be anything. As you know questions such as "find the next number in the sequence" are always invalid, as a real sequence is any injection from N into R. That is a sequence is only truely determined if you provide an instructions on how to get to the next one. If this were an arbitary sequence the next number might as well be Pi, since we were not given any properties of the sequence this is a valid answer.

Dave said...

My favorite used to be

1
11
21
1211
111221
what's the next line?

Daniel said...

There are 20 closed loops in my post.

Eric said...

Lmao, I actually got 2 right, nice!

Anonymous said...

oh my fucking god ppl!!! read the damn first comment and stop trying to impress the world with you made up "mathematic deduction skills" jesus t-rex riding christ!

Anonymous said...

Dave,

I think the answer is:

312211

and the line after that is:

13112221

Kyle Perkins said...

2581

The Eclectic said...

Easily solved by kids who haven't even entered school yet? Hogwash! This "couching" of the problem is distractive and clearly misleading since it really is not a Math problem. Sour grapes? Not at all! I still appreciate the problem and answer: it's a cool trick question!

Lemeshko said...

Hi, Eclectic,

Actually, whether the problem is a Math one or not, depends on how you approach to the solution. Some people here used mapping and topology for that. :)

twrriegel said...

Consider the following sequence...

2,4,6,...

What's next? As was stated earlier it can be anything.

Today I choose the next number to be 73. And here is a formula that makes it so...

(-1/3)(x-2)(x-3)(x-4) + 2(x-1)(x-3)(x-4) + (-3)(x-1)(x-2)(x-4) + (73/6)(x-1)(x-2)(x-3)

so.. when x=1 then

f(1)=(-1/3)(1-2)(1-3)(1-4) + 0 + 0 +0
f(1)=2

and when x=2

f(2)=0 + 2(2-1)(2-3)(2-4) + 0 + 0
f(2)=4

and when x=3

f(3)=0 + 0 + (-3)(3-1)(3-2)(3-4) + 0
f(3)=6

and magically :) when x=4

f(4)=0 + 0 + 0 + (73/6)(4-1)(4-2)(4-3)
f(4)=(73/6)(3)(2)(1)
f(4)=(73/6)(6)
f(4)=73

So we simply use the idea that any product with a zero in it will always be zero. This has the nice effect of cancelling out our big ugly formula.

A similar logic could be applied to the original sequence to make the answer anything we want it to be.

Fledermen64 said...

It is not a math problem. It is a viso-spatial problem that uses numbers. How the answer is obtained is to count the number of enclosed areas in each single digit. For example 8 has 2 enclosed regions. 9 and 0 both have only 1 along with 6 and 4. If you add up the number of enclosed region per four digit "number" you arrive at the answer.

For example 6764=3 because:
6 has one region
7 has zero regions
6 has one region
4 has one region
summed together there are 3 enclosed regions.

Not mathematics other than adding. For reference I am a junior in EE and have taking maths up to and including Calculus 3

Mr. Freund said...

I was stumped by a similar puzzle in 6th grade. It was called "Petals around the Rose" in which you would roll 5 6-sided dice. The person who new the trick would tell you the solution while repeating "petals around the rose". I'm sure you've got it now.

Fernando Casares said...

A similar problem is finding the next number in the following series:
1 11 21 1211 111221
This time, i believe there actually is NO mathematic solution for solving this.

Lemeshko said...

Hi, Fernando, I've also posted that one:

http://lemeshko.blogspot.com/2009/09/greatest-math-problem-ever-part-2.html

Anonymous said...

WAO THATS CLEVUR

Anonymous said...

It is extremely interesting for me to read the post. Thanks for it. I like such topics and everything that is connected to this matter. I would like to read a bit more on that blog soon.

Anonymous said...

The answer is 2. look at the circles of the numbers:).Romania rules..i hope:D

Anonymous said...

Look at the circles of the numbers forming each row;)
Romanian schools rule!

Anonymous said...

I found it in less than a minute.But the interesting thing is that if the comment abt 'school children' were not ter, i think i would not hav got t answer.

Rob said...

Wow... I feel really sorry for you PhDs who couldn't get this. I'm a post-grad mathematician myself (though not a PhD yet) and this was ridiculously easy to spot.

I hope you saved the receipts for all that tuition.

Lokesh Kumar said...

idiots....it's so simple ...
just count the total no. of circles..
just like a kid counts..

Anonymous said...

I'm coming to the party rather late but wanted to express what a great exercise this was. It certainly had a few of us at work performing mental gymnastics. It is surprising how hard it can be for some of us to deliberately think or perceive differently. Thanks for posting it.

I have to admit, I was a little taken aback by the posturing of some commenters and imagine it relates to either bruised egos, blind arrogance or lack of awareness of how people other than themselves think.

I think I understand those in the latter camp in that a right brain thinker has great difficulty in perceiving the way a left brain thinker would, and vice versa.

Similarly, I might be able to wrap my mind around the mentality of someone whose arrogance prevents them from imagining approaches other than theirs might be worthy of consideration.

But I have great difficulty in understanding the apparent anger some posters have expressed, as if they had somehow been victimized by either the puzzle, the solution or the comments.

Great discussion on whether this qualifies as math also. It's amazing how some reject it outright, which might explain their difficulty solving the problem, since they have difficulty in adapting their thinking. Typical authoritarian follower responses from those who like their world in a tight package, always constant and reliable, never to be interpreted as anything but their literal definition of it. Poor souls, really, as they will never discover anything new, just new ways of applying the status quo.

Julia Shekhtman said...

Haha! I just wasted two hours of my life that I will never get back, and the solution was so simple, it almost hurts!

Akhil Maloor said...

Could you guy's help me?

6-1*0+2/2= ?

I answered it 7

But one of my friend who is an accountant is arguing with me that the answer is 5

peternak hebat said...

The answer is ***