What number comes next?

[steve_bank]

2^3 = 8
8^3 = 512

2,8,512. The other numbers were noise.



110 130 __ 190

What is the missing number?

170... consecutive primes multiplied by 10?

The thread started with prime numbers. Now I will remember the first 20 primes.

 

[steve_bank]

111
222
333
444
555
706
817
???

Using my secret agent decoder ring I read 'Meet me at 2:00AM'

Spoiler

The difference table is
111,111,111,111,151,111

Assuming it repeats the next number is 928

 

[Emily Lake]

2^3 = 8
8^3 = 512

2,8,512. The other numbers were noise.



110 130 __ 190

What is the missing number?

170... consecutive primes multiplied by 10?

The thread started with prime numbers. Now I will remember the first 20 primes.

I kind of suck at these kind of pattern games. Give me more numbers in the series, and I do a lot better. But when there's only a few, I have a harder time - there's usually more than one method that can result in that short sequence, and it ends up being luck if I guess the correct one or not.

 

[steve_bank]

2^3 = 8
8^3 = 512

2,8,512. The other numbers were noise.



110 130 __ 190

What is the missing number?

170... consecutive primes multiplied by 10?

The thread started with prime numbers. Now I will remember the first 20 primes.

I kind of suck at these kind of pattern games. Give me more numbers in the series, and I do a lot better. But when there's only a few, I have a harder time - there's usually more than one method that can result in that short sequence, and it ends up being luck if I guess the correct one or not.

Yea, they are forms of mental exercise.

But we all do pattern recognition in different forms. Animals do it, a survival mechanism.

I stumbled on an old math problem book in a used book store years back. From around 1930s. People did math puzzles for fun. No TV, computers, video games.

It is a skill that can be learned by practice. I always have problems with contrived problems. I got motivated with real porbems.

The Mammoth Book of IQ Puzzles: Stretch... book by Compiled by Nathan Haselbauer

The Times MindGames Number and Logic... book by The Times

The NYT Wordle game is popualr

Wordle - A daily word game

Guess the hidden word in 6 tries. A new puzzle is available each day.

www.nytimes.com

Subscribe to New York Times Games

Upgrade your downtime with full access to The Crossword, The Mini, Spelling Bee and more.

www.nytimes.com

 

[bilby]

1
11
21
1,211
111,221
312,211
?

 

[James Brown]

1
11
21
1,211
111,221
312,211
13112221

 

[Swammerdami]

111
222
333
444
555
706
817
???

Congrats to steve who got this. What I came up with is the same 928, the numbers being multiples of 71₁₀ but in the mixed base (60,10,1) used in Babylon.

Speaking of Babylon ("And there followed another angel, saying, Babylon is fallen, is fallen, that great city, because she made all nations drink of the wine of the wrath of her fornication"), a problem that Emily's sequence solves is to avoid the infamous forbidden number which was revealed by Jesus Christ and signified unto His servant John:

And I stood upon the sand of the sea, and saw a beast rise up out of the sea, having seven heads and ten horns, and upon his horns ten crowns, and upon his heads the name of blasphemy.
...
And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world....
And I beheld another beast coming up out of the earth; and he had two horns like a lamb, and he spake as a dragon....
And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads: And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.

- - - - - - - - - - -
[Edit as per request]

 

[Swammerdami]

There is a simpler solution to the 111,222,333,444,555,706 puzzle; we simply need to add an extra 40 when we reach the Number of the Beast.
Why 40? That addend is prescribed by the very same chapter of Revelations!

I ... saw a beast rise up out of the sea, having seven heads and ten horns, and upon his horns ten crowns, and upon his heads the name of blasphemy.
...
... Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.

The 1 beast has 7 heads and 10 horns and 10 crowns and upon his heads 12, the number of the name of Blasphemy.
1+7+10+10+12 = 40 as Emily has noted.

Anyone who knoweth not that the Number of the Name of Blasphemy is 12 has simply not been paying attention:

D O N A L D J T R U M P​

1 2 3 4 5 6 7 8 9 10 11 12​

 

[Emily Lake]

2^3 = 8
8^3 = 512

2,8,512. The other numbers were noise.



110 130 __ 190

What is the missing number?

170... consecutive primes multiplied by 10?

The thread started with prime numbers. Now I will remember the first 20 primes.

I kind of suck at these kind of pattern games. Give me more numbers in the series, and I do a lot better. But when there's only a few, I have a harder time - there's usually more than one method that can result in that short sequence, and it ends up being luck if I guess the correct one or not.

Yea, they are forms of mental exercise.

But we all do pattern recognition in different forms. Animals do it, a survival mechanism.

I stumbled on an old math problem book in a used book store years back. From around 1930s. People did math puzzles for fun. No TV, computers, video games.

It is a skill that can be learned by practice. I always have problems with contrived problems. I got motivated with real porbems.

Clarifications... It's not a matter of lacking skill, it's usually a matter of there being multiple functions or patterns that fit a short snippet of the displayed sequence. It's usually a case of not having enough observations to be able to effectively exclude functions.

This is likely amplified by the fact that my entire career is statistical in nature, and on a really good day the best I'm going to get is an approximate fit that is good enough. There's a point where trying to get something that perfectly fits a relatively short series of observations is just not worth the effort, and isn't sufficient to predict future outcomes.

Consider the series I provider earlier:

111
222
333
444
555
706
817
???

I play nice I added 706 into that specifically so that the actual function could be accurately inferred. I could have provided a shorter snippet of 333, 444, 555 and let people try to figure it out. Most people would say that the next item in the series should be 666 - which isn't wrong given the information available. It's the easiest and most directly inferable function that fits the observed pattern. But it would be wrong, because I personally know the actual function I'm using, and nobody else does. That 706 is necessary to get the next item. It probably would have been more challenging if I'd only provided 444, 555, 706. I think the likelihood of people being able to figure out that 817 would be next would be fairly low, although not necessarily impossible.

Even if you get 928 and progress from there, what follows 1150? Does it go to 1301 or to 12101? If it's 1301... what happens when it gets to 2340?

That's more or less why I'm not great at these. However my brain is wired, I frequently end up with too many options that fit the limited data, then I get sucked into uncertainty about which one is the right one.. and I tap out and just don't care

 

[Emily Lake]

Congrats to steve who got this. What I came up with is the same 928, the numbers being multiples of 7110 but in the mixed base (60,10,1) used in Babylon.

Lol, this is what I mean - you came up with a complicated mathematical function that fits, even though it's actually a very simple pattern. The starting point is arbitrary, you could pick whatever seed you want. Then add eleven minutes and roll over at the top of the hour.

In my head, I'm using military time on a 24 hour clock, and when the day ends, I'd increment a day counter up to 7, then roll into a week counter... then into a year counter. So it ends up evolving into a YYYYWKH(24)MM+11.

 

[Emily Lake]

Here's a sequence I wrote down just a week ago, not as a puzzle but in preparation for a talk to Uni students. Guess not only the next number but the subject of the talk!
1
00
010
0110
00100
001100
?

Well, I can see that the most likely next number would be 0001000:

1
00
010
0110
00100
001100
0001000

But I don't have any idea about the subject... and my brain also thinks your sequence is off. My brain thinks it should go
1
11
010
0110
00100
001100

None of the other elements in the series lacks a 1, none have more than 1, each element with a single one inserts a 1 next to the prior 1, and the next step drops back to a single 1 but increments the count of zeroes on either end. I would speculate that it's some sort of branching exponential binary function... but I could certainly be wrong.

 

[Swammerdami]

What I came up with is the same 928, the numbers being multiples of 7110 [71₁₀] but in the mixed base (60,10,1) used in Babylon.

Lol, this is what I mean - you came up with a complicated mathematical function that fits, even though it's actually a very simple pattern....
... clock ...

FWIW, clock times DO USE the very same mixed base (60,10,1) as used in ancient Babylon.

But I prefer my 2nd solution where the number of the first Beast is added to contravene the dreaded Number of the second Beast.

 

[Bomb#20]

Clarifications... It's not a matter of lacking skill, it's usually a matter of there being multiple functions or patterns that fit a short snippet of the displayed sequence. It's usually a case of not having enough observations to be able to effectively exclude functions.

Exactly. In a good sequence puzzle the struggle should be to find even one rule matching the data, not to choose between multiple candidates on subjective grounds.

Consider the series I provider earlier:

111
222
333
444
555
706
817
???

I play nice I added 706 into that specifically so that the actual function could be accurately inferred. I could have provided a shorter snippet of 333, 444, 555 and let people try to figure it out. Most people would say that the next item in the series should be 666 - which isn't wrong given the information available. It's the easiest and most directly inferable function that fits the observed pattern. But it would be wrong, because I personally know the actual function I'm using, and nobody else does. That 706 is necessary to get the next item.

^^^^ This ^^^^

Here's a sequence I wrote down just a week ago, not as a puzzle but in preparation for a talk to Uni students. Guess not only the next number but the subject of the talk!
1
00
010
0110
00100
001100
?

Well, I can see that the most likely next number would be 0001000:

1
00
010
0110
00100
001100
0001000

But I don't have any idea about the subject... and my brain also thinks your sequence is off. My brain thinks it should go
1
11
010
0110
00100
001100

Whatever the solution is, it has to account for that 00 in the second line. The 00 serves the same function as your 706. So I think the 0001000 guess must be wrong -- it's the 666 in your puzzle.

For what it's worth, here's the most brutal sequence puzzle I've ever seen.

125 145 168 175 181 190 ...

 

[Swammerdami]

[Edit as per request]

The puzzle beginning 1, 00, 010 has been DELETED. It was wrong, invalid, false, erroneous, and mistaken. Any discussion of it would be too embarrassing. "I'll wanna roll myself up in a big ball and ..."

 

[steve_bank]

36
21
48
31
51
?

 

[Emily Lake]

[Edit as per request]

The puzzle beginning 1, 00, 010 has been DELETED. It was wrong, invalid, false, erroneous, and mistaken. Any discussion of it would be too embarrassing. "I'll wanna roll myself up in a big ball and ..."

Even with an error, I'm curious what the intended pattern was.