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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.



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.
Jun. 24th, 2010 01:01 pm (UTC)

2 out of 3. :)
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)
Jun. 24th, 2010 01:05 pm (UTC)

Damn, those went quicker than I expected!
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."
Jun. 24th, 2010 06:40 pm (UTC)
That's pretty tricky. Nice.
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?"
Jun. 24th, 2010 08:26 pm (UTC)
So, I only count 3 As, though I stopped there without checking the other letters requested.
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"
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.