We're playing a game in which you, the player, start with a number sequence. There is a rule governing which number comes next, and whoever determines the rule will recieve $10. Any one can play, but I tagged the people who i think will be most interested.

If you guess a number, I will tell you if it is correct, and if so, I will add it to the existing sequence. Please only guess one number each day. Please only guess one number at a time, dont try and fill in a section of the sequence.

If you guess the rule, I will tell you if you are correct or incorrect. If correct, you win $10. If incorrect, you may not guess the rule again for 3 days.

Original sequence:

2, 4, 6

The sequence so far is:

2, 4, 6, 10, 18, 30, 50, 82, 134, 218, 354, 622, 623, 630 47 comments Updated about a month ago

Craig Fleischman (Indiana) wrote at 7:44pm on July 13th, 2007 10? Message - Delete

Dan Margolis (Japan) wrote at 8:31pm on July 13th, 2007 7 Message - Delete

Jeff Borack wrote at 1:03am on July 14th, 2007 10 yes, 7 no Delete

Dan Margolis (Japan) wrote at 9:52am on July 14th, 2007 Its like fibonacci sequence except starting at 2. The next digit is the sum of the two previous digits. So it would be 2, 4, 6, 10, 16, 26, 42, 68, 110...

So... X0 = 2, X1 = 4, Xn = (Xn-1 + Xn-2) Message - Delete

Jeff Borack wrote at 12:16pm on July 14th, 2007 Incorrect Delete

Dan Margolis (Japan) wrote at 12:38pm on July 14th, 2007 Worth a shot...I can't deduce much from so few numbers... Message - Delete

Elliot Alyeshmerni wrote at 7:06pm on July 14th, 2007 im gonna go with 18 Message - Delete

Jeff Borack wrote at 8:24pm on July 14th, 2007 a job well done Delete

Yvette Monachino wrote at 8:08pm on July 15th, 2007 30 Message - Delete

Jeff Borack wrote at 10:47am on July 16th, 2007 30 works Delete

Yvette Monachino wrote at 11:06am on July 16th, 2007 50 Message - Delete

Jeff Borack wrote at 11:35am on July 16th, 2007 good Delete

Elliot Alyeshmerni wrote at 2:25pm on July 16th, 2007 82, still havent gotten the sequence down so this is a bit of a guess Message - Delete

Jeff Borack wrote at 2:33pm on July 16th, 2007 good Delete

Elliot Alyeshmerni wrote at 3:19pm on July 16th, 2007 i think we all got this sequence now.. Message - Delete

Jeff Borack wrote at 3:36pm on July 16th, 2007 i dont think anyone has it. but i welcome you to guess. If your right, $10. If your wrong, at least you'll save yvette! Good luck. Delete

Peter Dahlke wrote at 7:31pm on July 16th, 2007 134 next? Message - Delete

Jeff Borack wrote at 8:07pm on July 16th, 2007 yup Delete

Elliot Alyeshmerni wrote at 10:49pm on July 16th, 2007 218 Message - Delete

Jeff Borack wrote at 11:15pm on July 16th, 2007 218 Delete

Victor Baranowski wrote at 10:16am on July 17th, 2007 IDK where it started, but assuming we started with 2, 4, 6 the sequence is:

Xn = X (n-1) + [(X(n-1) - X(n-2)) + (X(n-2)-X(n-3))]

or something like that... Message - Delete

Jeff Borack wrote at 10:26am on July 17th, 2007 Interesting guess, I thought people were gonna say Xn = X(n-1)+X(n-2)+2, but both are wrong. Sorry Vic. The more interesting question is: why did it take so long for someone to guess? Is the reward for guessing the correct answer to low or is the penalty to high? Delete

Jeff Borack wrote at 10:45am on July 17th, 2007 I'm changing the rule of 1 rule guess/week. You can now guess once every three days. Numbers are still once a day even though elliot broke that rule and i accepted the number. Delete

Elliot Alyeshmerni wrote at 11:43am on July 17th, 2007 this a answer works for every number except 6 and 18, but i'll put it down anyway

X(n)=2X(n-1)-X(n-3) Message - Delete

Victor Baranowski wrote at 12:22pm on July 17th, 2007 Ya, that was similar to mine. Why the sequence goes from 10 to 18 is the tricky part of this whole thing, which makes me think the equation is going to be pretty ugly or wierd... maybe jeff made a mistake :P Message - Delete

Victor Baranowski wrote at 12:23pm on July 17th, 2007 Oh, and I might as well guess 354... Message - Delete

Jeff Borack wrote at 2:19pm on July 17th, 2007 a) the solution is beutiful b) i didn't make any mistakes yet c) 354 is good Delete

Victor Baranowski wrote at 2:46pm on July 17th, 2007 Can I cite a) in response to your b) ? Message - Delete

Jeff Borack wrote at 8:20pm on July 17th, 2007 Hmmmm, I'm not sure. It depends on when you think the mistake was made. Technically it did come before b), but i could also argue that the mistake what made when i clicked the "Add your comment" button.

a) the solution is... very nice and good b) i didn't make any mistakes in the number sequence yet. c) web browsers and AIM should have spell checkers. this isn't the 20th century anymore. Delete

Tait Kowalski wrote at 3:48pm on July 18th, 2007 Sequence goes x(n) = x(n-1)+2*x(n-3)

so the next number = 354 + 2*134 = 622

next number is 622 Message - Delete

Jeff Borack wrote at 4:41pm on July 18th, 2007 Welcome Tait! That is the wrong rule, but ill accept your guess at the next number. Delete

Elliot Alyeshmerni wrote at 6:28pm on July 19th, 2007 the next number is fuck you jeff, just give us the answer lol Message - Delete

Jeff Borack wrote at 6:47pm on July 19th, 2007 Sorry elliot, want me to call the Whaaaaaaaaaaaaaaaambulance? Delete

Victor Baranowski wrote at 4:29pm on July 22nd, 2007 is the next number 620? Message - Delete

Jeff Borack wrote at 7:23pm on July 22nd, 2007 hmm strange guess. 620 is not a number Delete

Victor Baranowski wrote at 8:46am on July 23rd, 2007 howabout 623? Message - Delete

Jeff Borack wrote at 12:40pm on July 23rd, 2007 : ) 623 is the next number Delete

Craig Fleischman (Indiana) wrote at 12:55pm on July 23rd, 2007 630? Message - Delete

Jeff Borack wrote at 12:59pm on July 23rd, 2007 630 is good Delete

Victor Baranowski wrote at 1:51pm on July 23rd, 2007 Solution: the next number is whatever number is guessed, as long as it is higher than the previously guessed number. Message - Delete

Jeff Borack wrote at 2:28pm on July 23rd, 2007 hahaha, yup. it took a lot of time but not a lot of guesses. i expected the guessing to to into the hundreds of thousands. do you accept paypal? Delete

Victor Baranowski wrote at 2:35pm on July 23rd, 2007 no, i accept shots and beers the next time we hang out. Message - Delete

Yvette Monachino wrote at 4:10pm on July 27th, 2007 that is the dumbest sequence i have ever heard of Message - Delete

Jeff Borack wrote at 5:08pm on July 27th, 2007 It's about thinking outside the box, yvette, something i wouldnt expect most MATH majors to understand! : p Victory for the engineers!!! Delete

Yvette Monachino wrote at 2:08pm on July 30th, 2007 aw thats a cute remark, knowing that you don't actually know what real math is i won't take that as an insult, and the only victory you accomplished is adding yourself to the long list of pompous engineers, so congrats :) Message - Delete

Jeff Borack wrote at 2:52pm on July 30th, 2007 While I might be pompous, I unfortunately can't be considered much of an engineer. I did bioengineering, which certainly doesnt count, and i've never actually engineered anything. Neither has vic, hes in law school.

It is true that i don't know what real math is (although i would love for you to teach me). However, I would imagine that real math does involve thinking outside the box on occasion. In this particular example, it required you to test a number you thought was not part of the sequence. If you believed you had found the sequence, and contintued to test numbers that fit that sequence, you would never derive the answer. By simply testing a number that does not appear to fall into the sequence, such as 2 million, it's easy to find the solution.

Does this sound like any 'real' math problems you have ever encountered?