# Rethinking this series on the syllabus

I assigned each person in my class the task of creating a number-sequence, however, 4 of the guys I usually consider to be leaders came back with baffling results.

Can you make sense of their work and tell me which number comes next in each?

Brian: 0,-0.5,4,0,0.5,1,1,?

Harry: 7,7,9,6,8,5,8,?

John: 0,1,4,-3,?

Xavier: 0,0.5,3,6,2,-4,5,-2,?

Hint 1?

During our periodic Shakespeare lessons, one of the boys brought some kind of flower to class, but it smelled awful. Of course, that just made him feel more the hero, so they kept coming, one after another.

• Hey, it's been sometime, could you add another hint? (: Commented Sep 26, 2019 at 21:17

It's taken nearly 3 years, but I think I have the answer at last... To complete the sequences requires the following numbers:

Brian: 0,-0.5,4,0,0.5,1,1,2
Harry: 7,7,9,6,8,5,8,8
John: 0,1,4,-3,-4
Xavier: 0,0.5,3,6,2,-4,5,-2,4

To explain how, I'll take you through my solving process in order...

Step 1a: The names

The first thing that jumped out at me on seeing the names was that:

Xavier is the surname of Professor X in the X-Men comic book and movie series. In fact, if we take the use of the word series in the title as a hint to focus on movie series, then looking at the other names we can identify other movie series which have a main character (leader, as per the text) of the same name:

Brian = Brian O'Conner from the Fast & Furious franchise;
Harry = Harry Potter;
John = John McClane from the Die Hard series.

Step 1b: The number of terms

At this point, looking at 'Harry' I noticed that:

this particular sequence has 8 terms - the same number as there are movies in the series (note, the movie series, not the book series). This suggested that each individual term relates to a specific movie in the series, most likely in order.

This was further backed up by noticing that there are 5 terms in the 'John' sequence - and 5 Die Hard movies. Furthermore, at the time of this puzzle being published there were 8 Fast & Furious movies (and 8 terms in the 'Brian' sequence). There are also many movies in the more complex timeline of the X-Men series and its many spin-offs (largely Wolverine-related), so with 9 terms in the 'Xavier' sequence I figured it was likely I could work out which ones were of interest once I knew the rules for generating the numbers...

Step 2a: Harry 7,7,9,6,8,5,8,?

Focussing on this sequence first - being the first I had recognised, and appearing to be the simplest with respect to its similar-ish values - I eventually found a rule that worked. The terms of this sequence relate to:

the number of syllables appearing after 'Harry Potter' in the movie title (which fits with the similar-sounding syllabus in the title):

Harry Potter and the Philosopher's Stone (7)
Harry Potter and the Chamber of Secrets (7)
Harry Potter and the Prisoner of Azkaban (9)
Harry Potter and the Goblet of Fire (6)
Harry Potter and the Order of the Phoenix (8)
Harry Potter and the Half-Blood Prince (5)
Harry Potter and the Deathly Hallows Part 1 (8)

So the final term must be:

Harry Potter and the Deathly Hallows Part 2 (8)

Step 2b: John 0,1,4,-3,?

Next to John, as the shortest sequence. Since the first term is '0', this suggests that the equivalent rule here is:

the number of syllables after 'Die Hard' in the movie title. BUT note there is a negative term - this corresponds to the movie 'Die Hard 4.0' which was released as 'Live Free or Die Hard' in North America, hereby suggesting that if words appear before 'Die Hard' they should be considered as worth negative one in the sum:

Die Hard (0)
Die Hard 2 (1)
Die Hard with a Vengeance (3)
Live Free or Die Hard (-3)

So the final term must be:

A Good Day to Die Hard (-4)

Step 2c: Brian 0,-0.5,4,0,0.5,1,1,?

Now we introduce positive and negative '0.5' terms, which we need to account for. My first thought was that:

here there were two key words in the titles, 'Fast' and 'Furious', and that anything after the second scores +1 and before the first scores -1 (similar to John's sequence), plus anything in between the two key words scores +0.5. However, there are two titles containing an ampersand (&) between the words 'Fast' and 'Furious' that do not appear to add an additional 0.5 to their total. Therefore, it seems that - additionally - non-alphanumeric characters are to be ignored, while letters and numbers count.

The Fast and the Furious (0)
2 Fast 2 Furious (-0.5)
The Fast and the Furious: Tokyo Drift (4 - note here that 'Tokyo' is pronounced with 3 syllables: To-ke-yo)
Fast & Furious (0)
Fast Five (0.5 - no 'Furious' here, but 'Five' still counts as falling 'between' the two key words)
Fast & Furious 6 (1)
Furious 7 (1)
The Fate of the Furious (2)

This means that the score for the last movie in the series at date of posting, The Fate of the Furious, should be calculated as 2 (since all words between the absent 'Fast' and 'Furious' score 0.5).

Step 2d: Xavier 0,0.5,3,6,2,-4,5,-2,?

Finally, to Xavier. First thing to do is identify the members of the series, which are likely the following:

X-Men (0)
X2 (0.5)
X-Men: The Last Stand (3)
X-Men Origins: Wolverine (6)
X-Men: First Class (2)
The Wolverine (-4)
X-Men: Days of Future Past (5)
X-Men: Apocalypse (4)

This way, the chronologically listed movies match all the scores if we apply the rules already identified for the other 3 sequences, and treat 'X' and 'Men' as the pre- and post- key words (like 'Fast' and Furious', previously). Notably, the sequence includes Deadpool (Feb 2016) and - although it could continue past the point at which it has stopped, with Logan and others - the movie that would appear in the place of the question mark is X-Men: Apocalypse (May 2016), which would score 4 points.

Summary:

In each case the following rules are at work:

A. Identify the two key words in the names of the movie series.
B. Syllables of other words in the title contribute 1 to the score if they appear after the second word, -1 if they appear before the first, or 0.5 if they appear in between.
C. Non-alphanumeric characters are ignored.

As presented at the top of this answer, this means that our answers should be:

Brian: 0,-0.5,4,0,0.5,1,1,2
Harry: 7,7,9,6,8,5,8,8
John: 0,1,4,-3,-4
Xavier: 0,0.5,3,6,2,-4,5,-2,4