What comes next...

[Will]

What comes next in this sequence:

8, 0, 2, 3, 4, 7, 0, 3, 5, 6...?

And why?

[Hardy Heinlin]

Here's a visualization of a suitable pattern. In my opinion, this kind of "sequence" questions in IQ tests are not accurately formulated; as there is no definition declared in advance, any answer is actually a correct answer. Similar to some pilot license test questions, you often need to know what the question designer had in mind, and not what the text literally asks and which sometimes doesn't contain sufficient information to allow just one answer.


8, 0,
>>>>> 2,
######### 3, 4,
7, 0,
>>>>> 3,
######### 5, 6,
6, 0,
>>>>> 4,
######### 7, 8,
5, 0,
>>>>> 5,
######### 9, 10,
4, 0,
>>>>> 6,
######### 11, 12,
3, 0,
>>>>> 7,
######### 13, 14,
2, 0,
>>>>> 8,
######### 15, 16,
1, 0,
>>>>> 9,
######### 17, 18,
0, 0,
>>>>> 10,
######### 19, 20,
-1, 0,
>>>>> 11,
######### 21, 22,

[Will]

Hint #1: It's not a strictly mathematical sequence.

[Hardy Heinlin]

Or split it in the middle and look at the vertical sequence in each digit column:

8, 0, 2, 3, 4
7, 0, 3, 5, 6
6, 0, 4, 7, 8
5, 0, 5, 9,10
...
...

[Will]

Hint #2: Germans, or people who have lived in Germany, are more likely than anyone else to recognize this.

[martin]

8, 0, 2, 3, 4, 7, 0, 3, 5, 6...?
...42
Correct!

Why? It is a random sequence! 

Seriously, this kind of test has worried me forever*. Isn't there always an infinite number of possible rules (and thus continuations) for any given sequence (and not only the one expected as the "correct" answer)?

1,3,5,7....
... 37
Correct!

Rule:"For three steps add 2, in the fourth step add 30..."

Or?


Cheers,
Martin

* and fueled my ambition to find in each test I encountered in a long career so far, at least one flaw (usually language), which doesn't kill the test only because people tend to agree and accept what the tester "means" over what he actually put down (or forgot to).

EDIT: Only after posting the above, I saw Hardy's comments (reply #1); it seems our ideas coincide remarkably.

[Will]

Agreed, there are an infinite number of possible rules in a game like this. But I'm thinking of a rule that allows you to predict with precision what the next twenty or thirty numbers in the series are.

Hint #3.A: The original series (8, 0, 2, 3, 4, 7, 0, 3, 5, 6) is a common abbreviation for this: 18, 20, 22, 23, 24, 27, 30, 33, 35, 36... (The original series omits the tens digit.)

Hint #3.B: The original series is commonly used because the un-abbreviated series takes a long time to say in German.

[Hardy Heinlin]

"Germany" is a very vague hint. That could be anything. Shoe sizes, phone numbers, names, geography, music scores, beer molecules ...

[mgeiss]

Although I'm from Germany, I had to look this one up. 
I'm probably too young (turning 39 in two weeks), but my father would have definitely recognized this. It's gone a bit out of fashion.

[Will]

It was pretty popular when I was living in Germany in 1987; even the kids in my high school were familiar. Nobody here in Chicago has any idea what it is.

Hint #4: Altenburg.

[Hardy Heinlin]

In 1987 I was in Greece. No wonder I don't know it.

[Will]

Hint #5: Εξηνταέξι, or μπουρλότο.

[Hardy Heinlin]

Something political?

[Will]

No politics involved. Entertainment.

[Jeroen Hoppenbrouwers]

I'm still at a total loss and I did spend time on this.  It's the "omits the tenths digit" that screws up all my ideas.

[Will]

Hint #6.A.: The sequence is 9 x n, 10 x n, 11 x n, 12 x n, plus some additional numbers that seems crazy and throw it off. Like 3 (which is 23, minus the tens digit, because that takes a long time to say in German).


Hint #6.B. The sequence is spoken out loud.

[Robert Staudinger]

8, 0, 2, 3, 4, 7, 0, 3, 5, 6...? >>>  0, 4, 5, 6, 8, 0, 4, 5, 9, 0, 3, 6, 0,....

These numbers are part of rules for a cardgame called Skat:
The sequence of possible Game Values: 18 - 20 - 22 - 23 - 24 - 27 - 30 - 33 - 35 - 36 - 40 - 44 - 45 - 46 - 48 - 50 - 54 - 55 - 59 - 60 - 63 - 66 - 70 ...


Enter following search pattern into Google: >>>   Altenburg "18 20 22 23 24"  <<< and you know the exact answer. This is a very popular game in Germany and some parts of Austria.

Greetings from LOWW

[Hardy Heinlin]

No wonder. I can't play Skat and don't know the rules.

I can play Mau Mau.

[Zapp]

As a mathematician and a teacher, I have a distinct hate for this kind of test.

When I was around 13, I encountered one of these sequences, something like 3, 7, 13, 21, 31 without any further information ... and was asked by my professor to write down the next 3 terms. I wrote something like

7943, 1234567, 42 (two randoms and the iconic 42 if you ask me)

He promptly marked it as wrong, and I said: "Well, I'm afraid you will have to PROVE me wrong". He was furious, because he didn't understand that I had given him the opportunity to recognize that I deserved the top mark. Too bad.

Teaching maths is not for everyone I'm afraid ....

Andrea

p.s. if you want to give the "right" answer to that (simple) question, I have to give you an additional piece of information: it is a polynomial sequence.

[Hardy Heinlin]

In my opinion, they just explain the task not accurately. I would describe the task like this: Find the continuous pattern in this sequence and continue this pattern.

It requires creativity as you need to develop various theories in advance, and then test your theories. My first theory would assume there are certain intervals between each number. Then test this theory, then note the intervals, then find a continuous pattern in these intervals. It's scientific thinking. Or Sherlock-Holmes-thinking :-) Have an idea, make a theory, test the theory. During the test discover something new, ask new questions, find new theories, test again. Until the whole picture makes sense.


|-|ardy