Sequence Pattern Challenges & Brainteasers

[indie]

One of my many time-wasting pursuits is to come up with number/letter pattern challenges. So, I thought I'd share a few with you today:

4, 18, 600, 35280 . . . ?

Y, A, X, H, ?

68, 528, 4160, 33024 . . . ?

Z, C, B, ?

:sombrero:

[indie]

No takers, eh? I thought at least a couple of iNTPs would be all over this.

[Zero Angel]

They are too difficult. I've tried several algorithms like counting back from x and incrementing by y, squaring and adding the root then rounding, etc. They are tough.

I am printing this topic off so I can figure it out offline.

[indie]

Hmm . . . when I was a member of the intp.org mailing list, I posted the first three, and a couple of people said they were "too easy." One of the gals said "I'd rather not be able to figure them out in my head." Go figure. . . (I think she was just being cocky, personally.) :)

[Edmond Zedo]

One of the gals said "I'd rather not be able to figure them out in my head." Go figure. . . (I think she was just being cocky, personally.) :)
What a moroness. If I can't figure it out in my head, I don't figure it out. The only one of yours I cracked is

:sombrero: = "Hot salsa! Yeeeowza!"

[QrioCT]

One of my many time-wasting pursuits is to come up with number/letter pattern challenges. So, I thought I'd share a few with you today:

4, 18, 600, 35280 . . . ?

Y, A, X, H, ?

68, 528, 4160, 33024 . . . ?

Z, C, B, ?

:sombrero:


Z, C, B, M. or is the pattern on the keyboard just a coincidence?

if i were right, then Y, A, X, H, M(pattern on keyboard again, except this ones very sloppy so i dont think i got it)

i have no time right now to think well(slacking off again while supposed to be working) so i'll come back again sometime to figure out the rest.

[purple13]

Y, A, X, H, V, O, U, V Am i right?

[indie]

Z, C, B, M. or is the pattern on the keyboard just a coincidence?

if i were right, then Y, A, X, H, M(pattern on keyboard again, except this ones very sloppy so i dont think i got it)

i have no time right now to think well(slacking off again while supposed to be working) so i'll come back again sometime to figure out the rest.

Qrio: You cracked the Z C B M one, very well done (yes, it is the keyboard thing). But, you are wrong about the Y A X H one. . . to assume that any of the sequences have anything in common is erroneous. Purple13 is (almost) right!

Keep trying. :)

[purple13]

oh, duh. I guess I don't know my alphabet backwards very well. Let's try this...

Y, A, X, H, W, O, V, V

[QrioCT]

Qrio: You cracked the Z C B M one, very well done (yes, it is the keyboard thing). But, you are wrong about the Y A X H one. . . to assume that any of the sequences have anything in common is erroneous. Purple13 is (almost) right!

Keep trying. :)

thought it was a sloppy assumption...but yay i got the first one. i think purple13 might be right this time about the second one tho. (even though i didnt check it completely it sounded right.)

[purple13]

yep, the first letter in the series goes backwards alphabetically from Y, and the second letter starts at A and steps +7 letters forward alphbetically.

[CapnEnnui]

68, 528, 4160, 33024 . . . ?
Is the next number 263168? And then the next 2101248?
It's the only pattern I could find... 68*8-4^2=528
528*8-4^3=4160
4160*8-4^4=33024
33024*8-4^5=263168...

So I guess it's the number before, multiplied by eight, then subtracted from it is four to the power of where that number is in the sequence... right?

[QrioCT]

wow. i was doing something like that with the other one but...dude how long did that take you?

[CapnEnnui]

15 minutes or so... I just noticed how every number was the same as the number before it multiplied by some number between 7.75 and 7.99. Then I started multiplying by 7 and seeing if i could add/subtract by some sort of pattern, and then I tried eight and found that the second one was the first times 8 minus 16, and tried it for the next, saw the difference was 64 this time, and voila.

I can't get that other one though.

[purple13]

Good job, Capn!

[QrioCT]

i know...wow.

[CapnEnnui]

I've got it! I think... OK it's kinda chaotic and probably wrong but....
4, 18, 600, 35280...
The first one is 2*2*1 = 4, with the one in there... uhh just cause?
So next is 3*3*2*1 = 18... the first number is used twice every time. Here's where I think my logic may fail...
What follows that is 5*5*4*3*2*1 = 600. Now, the problem here is that, instead of going up by one, it goes by two... this wouldn't be a problem IF the next sequence of multiples started with 8 (making it 2, 3, 5, 8, 12, etc) but it doesnt, which makes me unsure.
7*7*6*5*4*3*2*1 = 35280. NOW, you'll notice the first number for all of these is PRIME (1 isn't prime, but rather unique, so there's no 1)
So I'd assume the next number would be 11, which is the next prime number from 7, meaning the next number is 11*11*10*9*8*7*6*5*4*3*2*1 = 439084800
I'd otherwise say it's 9, but there's no logical reason for it to be 9. The only discernable pattern with 2, 3, 5, 7 is that they're the sequence of the the smallest positive prime numbers, meaning that 11 must logically come next.
Right?

[indie]

purple13 You were very close, but the number of letters between means nothing.

Y A X H W I V M U O T

is the answer. . . starting at the end of the alphabet, Y is the first symmetric letter we come across. Back to the beginning of the alphabet, A is the first. Back to the end of the alphabet, X is the next symmetric letter, back to the beginning, H is the next symmetric letter, and so on. :)

CapnEnnui Correct on both counts, though my explanation was meant to be a bit less messy . . . at least on the second one.

2 * 2! = 4
3 * 3! = 18
5 * 5! = 600
7 * 7! = 35280

11 * 11! = 439084800

or, in word form: p * p! where p is a prime > 1.

Good work.