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Fun With Numbers: Sequences October 18, 2010

Posted by nrhatch in People.
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220px-Arthur-Pyle_The_Enchanter_MerlinMath has logic and certainty behind it.

When you see the pattern, you can predict the next step in the progression.

It’s Black & White, without the endless shades of gray that predominate elsewhere in life.

Craving a bit of logical certainty?

Here are a few easy sequences to put order back into your day:

1)   1   4   9   16   25   36   ___   ___   81

2)  3   5   8    13   21    ___   ___   89   144

3)  8   ___  64   125   216   343   ___

4)   3   6   10   ___   21   28   ___   45   55

5)   2   4   8   16   32   ___   128   256   ___

6)   1   4   7   10   13   ___   19   22  ____

7)   3   9   27   81   243   ___   2187   ____

Answers tomorrow.  

NOTE:  Some answers may appear in the comments.  Don’t scroll down until you’ve solved the sequences . . . or have given up due to lack of sleep, lack of coffee, or lack of interest.  Cheers! 

Related posts:  Your Role Model *  The Laugh Calculator * Certainty and Symmetry * Attitude is EverythingSPOOKY: Last post = DCLXVI (666)

Comments

1. aardvarkian - October 18, 2010

1) 49, 64
2) 34, 55

…….

nrhatch - October 18, 2010

Excellent start, James . . .

2. cindy - October 18, 2010

You’ve got to be kidding … after being up half the night I can’t even think straight …

nrhatch - October 18, 2010

You are excused.

Besides, the bunny would probably eat your homework anyway. Bunnies eat everything!

3. loreen lee - October 18, 2010

The only one I can’t get is no. 3. Don’t see pattern, —YET!

nrhatch - October 18, 2010

Hey LL!

Glad to see you’re still popping in from time to time. 🙂

Good luck with #3.

4. Tammy McLeod - October 18, 2010

I am with Loreen – stumped by #3.

nrhatch - October 18, 2010

Number 3 is the least obvious. Glad that you solved the others.

5. andalibmarks - October 18, 2010

Should we write our answers down here or what?
I’m itching to do it!

*#*

nrhatch - October 18, 2010

You can post them here if you want. I’ll post a note above that some answers appear below.

The answers will be posted tomorrow at 8 am.

6. andalibmarks - October 18, 2010

OK, I have asked permission and now, here are my answers, I don’t know how many (if any) are correct but –

1) 49 ; 64
2) 34 ; 55
3) 27
4) 15 ; 36
5) 64 ; 512
6) 16 ; 25
7) 729 ; 6561

Well, that’s that.
I cannot wait until the morning!

*#*

nrhatch - October 18, 2010

Hey, you should work with numbers for a living!

Oh, wait, you do. 😉

On #3, there is an empty spot at the end of the sequence you haven’t filled in. But we both know you could. Cheers!

loreen lee - October 18, 2010

Would 413 be a candidate with the sequence, adding up the numbers in one given figure, in order, 8, 27(9) 64(10) etc. This would mean that there are alternative possibilities, except the sequence has to increase by the ration of l0 from number to number. i.e. 0-10; 10-100; l00-200 etc. Hope I have it. That’s my submission anyway….

nrhatch - October 18, 2010

Interesting pattern, LL

8 = 8
2+7 = 9
6+4 = 10
1+2+5 = 8
2+1+6 = 9
3+4+3 = 10
4+1+3 = 8

I hadn’t looked at it that way. And there is another solution.

7. loreen lee - October 18, 2010

Then it is the square root(?), first of 2 (2x2x2) then of 3 (3x3x3) etc. Gonna give up writing and get into math. grin grin. Thanks for the hint…

loreen lee - October 18, 2010

So the answer is 512, which incidentally adds up to the magic number 8. Now why is that? I’ll bet a pure mathematician would want to know why. Don’t you?

loreen lee - October 18, 2010

That’s don’t you think so too!!!! Ah! language.

nrhatch - October 18, 2010

Not the square root, or the square, but the cube:

2 = the square root of 4 and the cube root of 8
4 = 2 squared (or 2 to the 2nd power)
8 = 2 cubed (or 2 to the 3rd power)

And, LOL, LL at “Don’t you?” I expect that mathematician would know. But I don’t. 🙂

8. souldipper - October 18, 2010

ACK! My addiction. I won’t even look at it. It will take me to my logic problems or my sudokus and I’ll kiss the world goodbye.

nrhatch - October 18, 2010

I understand completely. Addictions are tough despite strong will power. 🙂

9. Mstrongair - October 18, 2010

Nancy,
This is great.

In exercise #3, is it possible to be 27 and 1000?

nrhatch - October 18, 2010

Why 1000?

10. Paula Tohline Calhoun - October 18, 2010

OK: I finally got around to doing this. Here are my provisional answers:
1)49; 64
2)43; 55
3)18; 413
4)15; 36
5)64; 512
6)16; 25

I say provisional because while I think I understand the pattern in each, it’s highly possible with my one hand I’ve made a typo, and I’m in too much of a hurry to go back and check it! How’s that for an excuse for a wrong answer? 😀
7)729; 2187; 6561

nrhatch - October 18, 2010

Well, you got some right . . . and some wrong.

11. andalibmarks - October 19, 2010

OMG!!!
How could I miss that Nancy!!
3) 27 ; 512

There.

*#*

12. andalibmarks - October 19, 2010

So where are the answers??!!

Oh, ahem, it’s not 8 am yet.
DAMN IT!! It’s just after midnight!
Oh the torture!
I guess you can see I absolutely LOVE numbers, right?

*#*

nrhatch - October 19, 2010

I do too! I’m going to have to find some new stuff for Fun with Numbers.

13. humm - October 19, 2010

49 64 square of no.s

34 55 previous no. + later no.

27 512 cubes

15 36 +3,+4,+5

64 512 *2

16 25 +3

729 6561 *3

nrhatch - October 19, 2010

Well done, humm! A perfect “10”!

I’ll see what other math puzzle I can find to challenge you all with.

14. Mstrongair - October 19, 2010

Nan,
This is quite fun!

Why 1000?

Every even number will follow a pattern of cubed 2 multiplied per cubed n where n is the place of the even number in the series.
Every odd number will follow a pattern of cubed prime number starting at 3.

8 = 2^3 x 1^3 27 = 3^3
64 = 2^3 x 2^3 125 = 5^3
216 = 2^3 x 3^3 343 = 7^3
1000 = 2^3 x 4^3 1331 = 11^3

nrhatch - October 22, 2010

Your explanation got caught in the Spam Filter. Guess WP didn’t like the look of all those numbers.

Interesting pattern but if I follow your lead, the answer is still 512, not 1000:

2x2x2= 8
4x4x4=64
8×64=512

15. m - October 25, 2010

You’re right, Nancy.
My bad. Sorry.
The place in the series for the even numbers that correspond to a prime number…

So the fourth term should be cubed two times cubed five equals a thousand.

nrhatch - October 25, 2010

Gotcha! Your solution works . . . and I wouldn’t have thought of it on my own. Nice job.


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