How do you solve number patterns?

[einstein]

This is a general question.

I've always been confused be patterns of numbers and trying to work out which numbers come next.

How do you solve number pattern problems?

Is it just a matter of memorizing the different kinds of number patterns, e.g. square numbers, triangular numbers, cube numbers, etc... and, if you dont recognize the pattern instantly, you just have to try each one on the patterns you know to see if any of them is the solution? If this is the way you do it, then what happens in tests where your time is limited? Surely you cant go through 20 different number patterns trying each one, one-by-one, until you find the answer. That would take to long.

So whats the deal with solving number patterns?

 

[tkhunny]

Usually, these exercises are a waste of time.

Having said that, learn what a "Difference" is. Simply subtracting successive values is a most useful tool.

Example

1, 2, 4, 7, 11 -- What's next?

(1) Differences:
2 - 1 = 1
4 - 2 = 2
7 - 4 = 3
11 - 7 = 4

Seeing a pattern, yet? If not, do it again.

(1) Differences:
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1

Now you're seeing a pattern.

This does not always expose a useful pattern, but it does rather often.

Note: If this pattern is useful, it must assume the continuation of the very few values available. This is a dubious assumption, at best.

 

[Deleted member 4993]

This is a general question.

I've always been confused be patterns of numbers and trying to work out which numbers come next.

How do you solve number pattern problems?

Is it just a matter of memorizing the different kinds of number patterns, e.g. square numbers, triangular numbers, cube numbers, etc... and, if you dont recognize the pattern instantly, you just have to try each one on the patterns you know to see if any of them is the solution? If this is the way you do it, then what happens in tests where your time is limited? Surely you cant go through 20 different number patterns trying each one, one-by-one, until you find the answer. That would take to long.

So whats the deal with solving number patterns?

I generally hate this type of problems.

What comes next

1, 2, 4, 8, 16, ....... most sane people will say 2⁵ = 32

But somebody else may have really meant to comment on Circle Division by Chords

then the series becomes 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ...

The correct but smarta$$ answer to the question "what comes next" should be "you tell me - what's in your mind"

 

[JeffM]

Disagreeing very slightly with Subhotosh Khan.

Seeing POSSIBLE patterns is a very useful heuristic when solving problems of many kinds.

The way these problems should be worded is

"Identify a plausible and simple formula that will generate this pattern of numbers."

There are an infinite number of algorithms that will generate a finite set of numbers. So I agree with SK's fundamental point that any problem that implies there is just one correct answer is a fundamentally stupid problem. Sadly, there are many stupid text books.

 

[tkhunny]

A man of my acquaintance ALWAYS answers "-2" for such problems.

Personally, I do my best to find something unexpected and DARE someone to call it wrong.

Bottom line: Do NOT stress over finding THE answer. Just find SOMETHING and PROVE IT.

 

[mmm4444bot]

How do you solve number pattern problems?

With grit. :cool:

 

[stapel]

I've always been confused be patterns of numbers and trying to work out which numbers come next.

How do you solve number pattern problems?

Is it just a matter of memorizing the different kinds of number patterns, e.g. square numbers, triangular numbers, cube numbers, etc... and, if you don't recognize the pattern instantly, you just have to try each one on the patterns you know to see if any of them is the solution? If this is the way you do it, then what happens in tests where your time is limited? Surely you cant go through 20 different number patterns trying each one, one-by-one, until you find the answer. That would take to long.

So whats the deal with solving number patterns?

Practice helps. If your class is studying "find the next number in the pattern" problems, try doing all of the exercises for which there are answers in the back. Try doing online examples, too; or get a different algebra book from your local library, and do the exercises in that. Practice will make a big difference in how familiar you are with the various typical patterns, and will go a long way in speeding up your insights while taking the test.

That said, yes, there are some methods for finding "the next number" (though, as has been mentioned above, "the" next number is whatever you can logically justify). You can review some of them here. The lesson at the link also has a page of "these aren't really 'math' patterns; they're dirty tricks often played on students in math classes", which you may find helpful, or at least comforting (as in, there's nothing "wrong" with you, that you can't find the [math] pattern, because the pattern isn't actually mathematical). ;)[/math]