Finish this sequence of equalities…
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 = ?
Hint: My wife found it immediately. Me, with my Ph.D. in Mathematics from the University of Montreal, and my B.Sc. in Mathematics from the University of Toronto, I could not find it. I also have a Mathematics publication record, at least according to AMS MathScinet. Yet, no luck.
Source: Misha Lemeshko
Montreal, Canada 
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Cute. That took me a minute or so before, thanks to your hint, I switched my maths brain off and saw it.
Those looking for another hint should think “topologically” (or perhaps homotopically).
Comment by Mark Reid — 10/1/2009 @ 18:08
I like that one. My wife didn’t get it, but I expect that’s because I bothered her when I introduced it to her.
Comment by Geoff Wozniak — 10/1/2009 @ 18:16
It’s the opposite of an open problem.
Comment by Daniel Tunkelang — 10/1/2009 @ 18:24
thanks God I don’t have a phd yet, I was able to solve it
Comment by phd student — 10/1/2009 @ 18:36
4444 = ?
Comment by Michael Lugo — 10/1/2009 @ 18:43
2581 = 2?
Comment by Karthik — 10/1/2009 @ 21:00
@Michael Lugo
4444 = 4 or 0, depending on which font you use.
Comment by Mark Reid — 11/1/2009 @ 2:44
2581 = 2 ?
Comment by David — 11/1/2009 @ 8:56
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 this mathematical problems if you like.
John
Comment by Sui Fai John Mak — 11/1/2009 @ 18:39
2
Comment by Stephen Downes — 11/1/2009 @ 19:35
2581 = 2
map 0, 6, and 9 to a value of ’1′
map 8 to a value of ’2′.
map any other digit to ’0′
sum up mapped digit values of the left number and you obtain the number on the right.
examples:
8809 = 6: 8(2) + 8(2) + 0(1) + 9(1) = 6
2222 = 0: 2(0) + 2(0) + 2(0) + 2(0) = 0
6855 = 3: 6(1) + 8(2) + 5(0) + 5(0) = 0
therefore,
2581 = 2: 2(0) + 5(0) + 8(2) + 1(0) = 2
Comment by David — 11/1/2009 @ 20:31
I challenged a friend with this problem and he answered: “just count the number of circles found on the left”.
I prefer his solution to mine.
Comment by David — 12/1/2009 @ 12:42
Just a few words of rambling on that.
“Salience of artifacts upon a shifted representation of the problem”
The question remains, how do we (usually) spot the fruitful representation?
Comment by Kevembuangga — 13/1/2009 @ 4:23
“My wife solved it” is much too great of a hint. Took about two seconds to solve it after I read that.
Comment by Paranoid — 13/1/2009 @ 20:35
(am I sexist or just psychologically well-educated?)
Comment by Paranoid — 13/1/2009 @ 20:36
First Betti number of the collection of digits, thought of as a topological space!
Comment by Sammy — 1/3/2009 @ 19:17