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Stop! Puzzle Time!

Time for a little bit of fun. :) Since these were shared with me, I'm sharing them onward!

1) What is the next in the sequence, and why?

1, 3, 7, 12, 18, 26, 35, 45, 56, 69, ____

2) What is the next in the sequence, and why?

1, 11, 21, 1211, 111221, 312211, 13112221, ____

3) Try to find a sentence using exactly four a's, three c's, three d's, thirty-two e's, eight f's, four g's, seven h's, twelve i's, three l's, nineteen n's, nine o's, one p, one q, nine r's, twenty-four s's, eighteen t's, five u's, seven v's, five w's, two x's, and five y's.

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Comments

( 16 Notes — Write a Footnote )
scifantasy
Jun. 24th, 2010 12:59 pm (UTC)
2) 1113213211. It's the description of the previous number--one 1, one 3, two 1, three 2, one 1.
3) Why should I? You already did.
stormfeather
Jun. 24th, 2010 01:01 pm (UTC)
Woot!

2 out of 3. :)
scifantasy
Jun. 24th, 2010 01:03 pm (UTC)
And here's the third one: 83. It's a straight-up "add the next number"--except that if your number is in the sequence, you skip it. Hence, 1+2=3, but since 3 is in the system, you go to 3+4=7, 7+5=12, 12+6=18, but you add 18+8 because 7 is in the sequence. So, after 56+13=69, you go 69+14=83.

Edited at 2010-06-24 01:03 pm (UTC)
stormfeather
Jun. 24th, 2010 01:05 pm (UTC)
*applause*

Damn, those went quicker than I expected!
scifantasy
Jun. 24th, 2010 01:08 pm (UTC)
Well, 2 and 3 seemed very familiar--it wasn't "oh, I remember this puzzle, I know the answer," but it was more like "OK, I think there's a trick in 3--what else can it be? Of course" and "2...haven't I seen this before? Don't remember. One, then two ones--wait, that next one is 'two one'..."

As to 1, I'd determined the addition pattern easily enough, and I was just saying to myself "why are three, seven, and twelve skipped--wait, three, seven, and twelve? Of course."
khedron
Jun. 24th, 2010 06:40 pm (UTC)
That's pretty tricky. Nice.
khedron
Jun. 24th, 2010 06:39 pm (UTC)
3) Why should I? You already did.

Yeah, as I made myself read through the entire thing, I was thinking, "Damn, that's far too demanding. So what's the short-cut?"
pokeypenguin
Jun. 24th, 2010 08:26 pm (UTC)
So, I only count 3 As, though I stopped there without checking the other letters requested.
scifantasy
Jun. 24th, 2010 08:36 pm (UTC)
First a: "a sentence"
Second a: "exactly"
Third a: "four a's"
Fourth a: "and five y's"
pokeypenguin
Jun. 24th, 2010 08:52 pm (UTC)
That bastard of an 'and', my brain blanked it as non-existent when I was counting Ds, too.
donaithnen
Jun. 24th, 2010 07:11 pm (UTC)
Trying to respond without looking at anyone else said...

Well my first order answer for the first one is "83", because the sequence is incrementing by a number that increments by either 2 or 1 each step, and _that_ pattern seems to be following a pattern where the number of 1's between each 2 increases by one with each cycle. And after 83 should be 98, 114, 131 and 150.

However that's probably not actually the correct pattern :)
donaithnen
Jun. 24th, 2010 08:19 pm (UTC)
Re: Trying to respond without looking at anyone else said...
Okay, tried lots of different things with the second one with no success so far, so i'll just skip to the third one.

"Try to find a sentence using exactly four a's, three c's, three d's, thirty-two e's, eight f's, four g's, seven h's, twelve i's, three l's, nineteen n's, nine o's, one p, one q, nine r's, twenty-four s's, eighteen t's, five u's, seven v's, five w's, two x's, and five y's." Also, 19 apostrophes, 48 spaces, 20 commas, and one period :)
donaithnen
Jun. 24th, 2010 08:23 pm (UTC)
Re: Trying to respond without looking at anyone else said...
Oh wait, thinking through the third one was enough to clue me in on the second one!

1113213211, if i'm counting right at least.

Perhaps i should go back and look at the first one again now :)
stormfeather
Jun. 25th, 2010 02:01 am (UTC)
Re: Trying to respond without looking at anyone else said...
Hah, yeah, first one wasn't what I was looking for, but yeah, I never even thought about the second and third ones being paired together to hint at each other. XD
(Deleted comment)
stormfeather
Jun. 25th, 2010 02:03 am (UTC)
Having fun? ;)
( 16 Notes — Write a Footnote )