# Solve this number pattern problem **URL:** \ **Category:** Factual Questions\ **Created:** [January 31, 2003, 11:28pm UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984 "2003-01-31T23:28:53Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Grim\_Beaker](https://avatars.discourse-cdn.com/v4/letter/g/46a35a/32.png) [@Grim\_Beaker](https://boards.straightdope.com/u/Grim_Beaker)\ **Post date:** [January 31, 2003, 11:28pm UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/1 "2003-01-31T23:28:53Z")
So my 11 year old son asked me for some help on his math homework yesterday. The questions he was having problems with are all number pattern problems (a simple example: 1,2,4,8,16,? Whats the next number in the pattern?). 5 out of 6 were easy to decipher, no big deal. The 6th has resisted the 45 minutes I’ve spent peering at it. I already sent him to school with a large question mark in the place of that question on his homework so don’t worry that you’ll be doing my 5th grader’s homework for him. In any case this problem (assuming it’s not a typo in the book) seems to be way out of the league of your run of the mill 11 year old. So help me out here Dopers. What are the missing numbers to the following sequence (X’s indicate numbers that need to be filled in to complete the pattern)? X, 2, 3, X, 6, 12, 16, 24, 36, X, 72, 144 Grim ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [January 31, 2003, 11:57pm UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/2 "2003-01-31T23:57:05Z")
1, 2, 3, 4, 6, 12, 16, 24, 36, 48, 72, 144 Took me a while! The sequence is factors of 144 paired from the ends inward: 1 x 144 = 144, 2 x 72 = 144, 3 x 48 = 144… I think. It breaks down at 12 x 16. But I can’t see any other obvious pattern. Maybe 16 is supposed to be 12? ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [February 1, 2003, 12:00am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/3 "2003-02-01T00:00:17Z")
Well, are you sure it’s not a typo? For example, if the problem were “X, 2, 3, X, 6, **9** , 12, 16, 24, 36, X, 72, 144” then **Q.E.D.** would be right on the money. If it’s not a typo, I’m stumped for the moment. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 1, 2003, 12:00am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/4 "2003-02-01T00:00:37Z")
I sure don’t see it… The numbers appear to be derived by taking the previous number, and multiplying it by 2, by 1.5, or by 1.25, but I don’t see a pattern. Trinopus ---
**Author:** ![Grim\_Beaker](https://avatars.discourse-cdn.com/v4/letter/g/46a35a/32.png) [@Grim\_Beaker](https://boards.straightdope.com/u/Grim_Beaker)\ **Post date:** [February 1, 2003, 12:00am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/5 "2003-02-01T00:00:40Z")
Whoops! I forgot an X in the sequence. Here it is again (correctly): X, 2, 3, X, 6, **X** , 12, 16, 24, 36, X, 72, 144 Grim ---
**Author:** ![II\_Gyan\_II](https://avatars.discourse-cdn.com/v4/letter/i/bbe5ce/32.png) [@II\_Gyan\_II](https://boards.straightdope.com/u/II_Gyan_II)\ **Post date:** [February 1, 2003, 12:01am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/6 "2003-02-01T00:01:06Z")
> [@](#): > > \*Originally posted by Q.E.D. \* > \*\*1, 2, 3, 4, 6, 12, 16, 24, 36, 48, 72, 144 > > Took me a while! The sequence is factors of 144 paired from the ends inward: 1 x 144 = 144, 2 x 72 = 144, 3 x 48 = 144… > > I think. It breaks down at 12 x 16. But I can’t see any other obvious pattern. Maybe 16 is supposed to be 12? \*\* More likely, there has to be a 9 in between 6 and 12. ---
**Author:** ![Grim\_Beaker](https://avatars.discourse-cdn.com/v4/letter/g/46a35a/32.png) [@Grim\_Beaker](https://boards.straightdope.com/u/Grim_Beaker)\ **Post date:** [February 1, 2003, 12:02am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/7 "2003-02-01T00:02:43Z")
That’s it **Math Geek**! Now tell me… is this a pattern that most 11 year olds are going to see? Grim ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 1, 2003, 12:03am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/8 "2003-02-01T00:03:51Z")
Yep, that’s it. That missing X is a 9, and the sequence holds the way I figured: 1, 2, 3, 4, 6, 9, 12, 16, 24, 36, 48, 72, 144 ---
**Author:** ![Grim\_Beaker](https://avatars.discourse-cdn.com/v4/letter/g/46a35a/32.png) [@Grim\_Beaker](https://boards.straightdope.com/u/Grim_Beaker)\ **Post date:** [February 1, 2003, 12:04am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/9 "2003-02-01T00:04:56Z")
Good work **Q.E.D.**. Now that it’s been shown to me it seems so simple. Seems like that’s the way it always is though with these types of problems… \ ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 1, 2003, 12:05am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/10 "2003-02-01T00:05:21Z")
I think that 8 and 18 should also have been included. Another oversight, maybe? ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 1, 2003, 12:05am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/11 "2003-02-01T00:05:22Z")
Hey, why does **he** get the credit? :eek: I spent a good 15 minutes on that thing! ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 1, 2003, 12:06am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/12 "2003-02-01T00:06:30Z")
Grrrrrrrrrr…slow updates. You’re welcome. (it was kinda fun. hehe) ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [February 1, 2003, 12:06am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/13 "2003-02-01T00:06:32Z")
The problem with number patterns like this is that, in fact, we could come up with lots of formulas. In fact, there is a theorem in number theory that, given any sequence of real numbers x[sub]1[/sub], x[sub]2[/sub], x[sub]3[/sub], … x[sub]n[/sub], and any real number y, you can find a formula so that x[sub]n+1[/sub] = y. A quick example, what’s next in the sequence 1, 3, 5, 7 … (a) 9 (b) 11 © 8 OK, if it’s a sequence of odd numbers, the next number is 9. If it’s a sequence of odd prime numbers, the next number is 11. And if it’s a sequence of numbers that have the letter “e” in their alpha-name, then the next number is 8. I hate these pattern problems. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 1, 2003, 12:09am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/14 "2003-02-01T00:09:35Z")
True that there are often many correct solutions, and a good grader will give credit for any of them, as long as they’re not too contrived. However, it is often the case that there is one simplest solution. As long as you acknowledge that you’re looking for the best solution, and not the only solution, I don’t mind these kind of things on standardized tests and the like. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 1, 2003, 12:09am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/15 "2003-02-01T00:09:43Z")
I got yer pattern problem… **right here, buddy**! What comes next in this letter sequence: ZOTTFFSSE? ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [February 1, 2003, 12:12am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/16 "2003-02-01T00:12:42Z")
N(ine) ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 1, 2003, 12:14am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/17 "2003-02-01T00:14:38Z")
_ding ding ding_ Give the man a see-gar! ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [February 1, 2003, 12:22am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/18 "2003-02-01T00:22:44Z")
\<\< a good grader will give credit for any of them, as long as they’re not too contrived…it is often the case that there is one simplest solution. As long as you acknowledge that you’re looking for the best solution…\>\> And which is the “best” solution or the “simplest” solution to the sequence 1, 3, 5, 7… that I posed above? Bah, I say, humbug. People who pose these kind of questions on tests are people who don’t understand mathematics. Or people who penalize students who think deeper than others. And I strongly disagree that “a good grader” will give credit for blah blah. Most graders of these questions are computers, who read only a “right” answer. And most teachers who pose these questions don’t ASK the students to EXPLAIN their answer, they just ask “what comes next.” ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 1, 2003, 12:25am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/19 "2003-02-01T00:25:39Z")
> [@](#): > > \*Originally posted by C K Dexter Haven \* > Take the sequence 1, 4, 9, 16, 25, 36… What comes next? > Well, we’re adding the odd numbers (+3, +5, +7, +9, + 11…), so the next number is 49. I also get that by squaring the integers, so the next number is 64. Which solution is “best” or “simplest”? Well, if my only choices are 47 and 64, I’m in trouble. I would have to go with 49 for either one. You do realize that those two algorithms produce the same sequence, right? As for the other sequence you gave, I would say 9. Odd number is a simpler concept than odd prime number. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 1, 2003, 12:27am UTC](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984/20 "2003-02-01T00:27:14Z")
Wait a minute, what the heck? I swear when I quoted that, it said 47, not 49. I guess I’m just not reading very carefully. Sorry. But 49 is still the right answer, either way. [Next page](https://boards.straightdope.com/t/solve-this-number-pattern-problem/151984.md?page=2)