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Fun With Numbers: Sequences ~ Answers October 19, 2010

Posted by nrhatch in People.

Huey,-Dewey-And-LouieAs promised, here are the answers to  Fun with Numbers: Sequences posted yesterday:

1)  1  4  9  16  25 36  49  64  81

These numbers are simple “squares” from 1×1=1 through 9×9=81

2)  3  5  8  13  21 34 55 89 144

This sequence requires adding the preceding two numbers to determine the next number in the sequence:

5+8=13, 8+13=21, 13+21=34, 21+34=55

3)  8  27  64  125  216  343  512

These are all cubes, from 2x2x2=8 through 8x8x8=512.  But see Loreen’s comments on Fun with Numbers: Sequences for an interesting pattern she observed. 

4)  3  6  10  15  21  28  36  45  55

This sequence adds increasing integers (3, 4, 5, 6 up to 10) to the preceding number:  3+3=6+4=10+5=15+6 =21+7=28+8=36

5)  2  4 8  16  32 64  128  256 512

Multiply by 2 all the way through the sequence, ending with 2 to the 9th power:  2x2x2x2x2x2x2x2x2=512

6)  1  4 7  10 13  16  19  22  25

Add “3” all the way through the sequence.

Mickey-OK7)  3  9  27  81  243  729  2187  6561

Multiply by “3” all the way through the sequence, ending with 3 to the 8th power:


So, how did you do?  Are you going to give Einstein a run for his money in the math department?


1. andalibmarks - October 19, 2010

I have been waiting for these since just after 12 this morning!!!!

Now my curiosity has been silenced.
Thanks for this Nancy.

It was really fun!!


nrhatch - October 19, 2010

A perfect score! Does that make you a “10”?

2. cindy - October 19, 2010

Of course I got them all right.
*Cin crosses fingers behind back*

nrhatch - October 19, 2010

I’ll get you playing one of these days. 🙂

souldipper - October 19, 2010

Nancy, you’re dealing with a woman who can’t control a rooster, for goodness sake. I bet she feeds it Chardonnay.

nrhatch - October 19, 2010

Maybe that’s why it slept so late the other day . . . hungover from unwanted chardonnay!

3. loreen lee - October 19, 2010

Thanks nr. It was fun competing with the mathematicians. Think I understand now where the numerology people get the justification for their pursuits. Checked out the finding of patterns, in a few others, and found some. But this hasn’t the necessity of real mathematics for some reason. There were alternatives with #3, and my parameter was incorrect. Thanks for telling us that 3. is a cube. Actually thought ‘by myself’ that a ‘square cube’ would make sense, but didn’t know what to call it. square cube? What a contradiction! cube root? maybe. Thanks again.

nrhatch - October 19, 2010

Squares are 2 sides: 2×2 or 7×7
Cubes are 3 sided: 2x2x2 or 8x8x8

2 = the square root of 4 and the cube root of 8

49 = 7 squared (or 7 to the 2nd power)
8 = 2 cubed (or 2 to the 3rd power)

Glad you enjoyed the challenge.

As I told Andi, I’ll have to dig up some more Fun with Numbers for when we get tired of playing with words.

4. andalibmarks - October 19, 2010

Oh yeah!
Bring it on, baby!!

5. Paula Tohline Calhoun - October 19, 2010

OK: My #2 answer really was a typo – I think I put in 43 & 55, instead of 34 & 55. It’s right in my notes, anyway, so I don’t feel bad about that!

As for #3 – My sequence was the numbers successively adding from 8 to 9 to 10, then back to 8, 9, 10, then ending with 8. (Don’t know how far you could go with this.) The succeeding number has to be the nearest number that equals 8, so I guess Loreen and I were on the same track? Interesting how the correct answer also works, just not the next available one. Great minds, Loreen!

nrhatch - October 19, 2010

To me, the cubes seemed obvious. So I never considered other patterns. How mundane! 😉

I’m impressed with you and LL for thinking outside the box.

6. loreen lee - October 19, 2010

Just thinking here, trying to be an Einstein with the math! grin grin. I think it has to do with limits, in this case l and l0, which reduces to l.
You don’t have a cube of one. So two and three as cubes express as eight and twenty-seven. But when you get to four you are back at unity, expressed not as a l but as a ten. It is my speculative philosophical way-out thinking, that this pattern would repeat, infinitely, each time the product of ten reducing to one or unity. No wonder the numerologists have so much fun. Wish I had an expert opinion on this. But hey! I’m entitled to my ‘opinion’ and ‘imagination’. grin grin.

nrhatch - October 19, 2010

You’re right. The cube of 1 is 1. So the pattern would be: 1, 8, 9, 1, 8, 9, etc.

1 = 1
8 = 8
2+7 = 9
6+4 = 10 = 1+0 = 1
1+2+5 = 8
2+1+6 = 9
3+4+3 = 10 = 1
5+1+2 = 8
729 = 9
1000 = 1
1331 = 8

Very cool!

loreen lee - October 19, 2010

Nope, I think the pattern would be one, two, three, one, two three, if you reduced the numbers as they do in numerology. I like it metaphysically, because it might be one of the underpinnings of the Trinity, and the use of three for concept formation in some philosophers, etc. Three is a very useful endpoint in the literature. It’s fun to see a math that ‘backs it up. The eight reduced to 2, and the 9 reduces to 3. though. Finding them as the numerologists do is not based on the same constraints, and necessities of true mathematics, though, I believe. They do not use the same method in finding their solutions. Mathematicians don’t ‘play’ with numbers, as I understand it, as the numerologists do, taking advantage and pushing the limits on the application of true mathematics. My understanding….. Yes? (Gotta learn to be a mathematician and think more ‘in the box’, to use a metaphor!

7. Paula Tohline Calhoun - October 19, 2010

Except: the next possible sequence after 343 is 350, and after 512 is 513. I know there are probably some I’ve left off or skipped. It is an interesting pattern, however. I think I see another one forming, I’ll puzzle on it for a while (maybe), but this is not so much an example of out of the box thinking as it is thinking and reasoning of a person who has absolutely NO concept of math and how it works from an abstract point of view. I did wonderfully well in algebra, because there were rules I could memorize and follow (as long as I remembered the right rules at the right time – not always a given with me!).

My true math problems surfaced when geometry came along in school. I cannot make heads of tails of it, and the same goes for physics and calculus. I wish there were someone out there who had techniques for teaching people with my type of reasoning patterns (or skills, as it were). I would really LOVE to understand mathematics, and I would spend the time with the right teacher in order to learn it. I think it would open up a whole new world for me. . . *sigh*

loreen lee - October 19, 2010

I think we have to remember that the cube is a spatial concept. I think it’s math to reduce 27 to 3 and 64 to 4, as the base of the cube, but that it is numerology, to add up the numbers and get 8, 9, and l0 or 1. Somehow, with numerology, there is always a puzzling question that it ‘doesn’t have to be that way’. I prefer math. Wish like you Paula, I could understand it better. We are certainly alike in that respect. After all, I had to struggle for the concept of a cube, which is one of the reasons I came up with the ‘metaphysical numerology solution’. This solution does ‘work’ though if applied to the math sequence; that I find amazing! But yes, it will reduce to 8, 9, and 1, which suggests to me that ‘something is wrong’ with the thesis!

nrhatch - October 19, 2010

I know very little about Numerology, so I can’t comment on it.

Still impressed that you and Paula tackled the sequence from the “opposite direction” and discovered some interesting hidden patterns.

8. booksphotographsandartwork - October 19, 2010

Fun with Numbers! Ha! Thats just not possible. 🙂

nrhatch - October 19, 2010

All I have to do is look at this photo of Einstein and I start smiling. 🙂

9. Mstrongair - October 20, 2010

Who is the other guy?

nrhatch - October 20, 2010

David Ben Gurion . . . former Prime Minister to Israel.

10. Mstrongair - October 25, 2010


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