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In technical papers I often see text like this.

Finally, the goal is to determine x. The three ways of achieving this are the following: The blue method involves tying your shoelaces. The pink method requires you to first go to the shops and buy a bunch of bananas. The purple method is really quite complicated and will take a long time to describe.

What is the proper way to write this? In particular, should the colon simply be a full stop, should the sentences read more like "The pink method, which requires[...]" and should the final sentence start differently?

I should perhaps have added that this needs to all be in one paragraph. There is not enough space to set it out as a numbered list.

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Finally, the goal is to determine x. The three ways of achieving this are the following: (1) the blue method involves tying your shoelaces; (2) the pink method requires you to first go to the shops and buy a bunch of bananas; (3) the purple method is really quite complicated and will take a long time to describe.

To separate the listed items, you can use commas, semicolons, or periods. Also using numbers to segment your list grants you the freedom of writing multiple sentences per list item. Contrarily, if you prefer not to use numbers for segmentation, your list items should not exceed one sentence in length, as this would likely add confusion.

Capitalization rules for a list after a colon are imprecise (see here and here). However, you must maintain consistency for whatever capitalization pattern you choose. For example, the first word of each list item can be capitalized or not (unless you choose to separate list items with a period - in which case you should definitely capitalize the following word). Whether to capitalize the first word following a colon is also your choice (but maintain consistency). The only exception to the consistency rule is if you separate using periods, the first list item after the colon does not necessarily have to be capitalized.

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  • Thank you. That looks like a good solution. Although if you are never going to refer to the numbers, are they perhaps not a little too much? Can we simply remove them and if so, are the semi-colons still correct?
    – Simd
    Commented Mar 28, 2015 at 20:48
  • You can either use commas or semicolons. In fact, if you utilize the numbers, you can even use periods. However, I do prefer numbers (even if they will never be referred to) because it clearly distinguishes each of the three ways. Furthermore, if any of your numbered items were to exceed the length of a sentence, the numbers would be invaluable in providing the needed clarity as to the beginning and end of each list item.
    – Mike
    Commented Mar 28, 2015 at 20:52
  • The numbered items are indeed likely to be long. What do you do if a numbered item is more than one sentence long? It seems odd to start a numbered item with a lower case letter but to have a capital within the item. Or am I just being too fussy ?
    – Simd
    Commented Mar 28, 2015 at 20:53
  • Using numbers solves that problem, because then you can use periods within a numbered item as much as you'd like.
    – Mike
    Commented Mar 28, 2015 at 20:54
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    Then you may use a capital letter instead: grammar.ccc.commnet.edu/grammar/marks/colon.htm. Also, Rule #3 here: grammarbook.com/punctuation/colons.asp (which essentially says, just be consistent).
    – Mike
    Commented Mar 28, 2015 at 20:59
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Commas

Handbook of Parametric and Nonparametric Statistical ... - Page 95 David J. Sheskin - 2003

Specifically, if we designate the four students A, B, C, and D, the six ways are as follows: A and B, A and C, A and D, B and C, B and D, C and D.

Commas, counted/indexed

The Corsini Encyclopedia of Psychology - Volume 2 - Page 682 Irving B. Weiner, ‎W. Edward Craighead - 2010

Notwithstanding the common association of forensic with autopsies as in forensic medicine, the three ways are (1) psychology by the law, (2) psychology in the law, and (3) psychology of the law.

Bullets

Pro Jakarta Commons - Page 108 Harshad Oak - 2004 - ‎Preview -

The three ways are as follows:
• Using an XML file to define pool settings
• Creating an instance of PoolingDriver
• Creating an instance of PoolingDataSource

Semicolons

See the example at this link:

Get Set for Religious Studies By Dominic Corrywright, Peggy Morgan

Semicolons are also useful for lists where the items consist of more than one word [...]

See more commentary and examples:

Plain Language for Lawyers edited by Michele M. Asprey

The Facts on File Guide to Style By Martin H. Manser

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  • In "Specifically, if we designate the four students A, B, C, and D, the six ways are as follows: A and B, A and C, A and D, B and C, B and D, C and D." if you replace A with "apple" in its normal English usage, should it start with a capital letter after the colon?
    – Simd
    Commented Mar 28, 2015 at 20:57
  • See the first reference at the end: Plain Language for Lawyers
    – Marius Hancu
    Commented Mar 28, 2015 at 21:06
  • Also, if using Chicago, buy an subscription online to CMOS. Offers access to the forum for only $40/year. Very good for any editing.
    – Marius Hancu
    Commented Mar 28, 2015 at 21:14
  • Commas may not work if they are also needed within items so of this nice list of options I would prefer semicolons (though bulleted lists have their place).
    – Chris H
    Commented Mar 28, 2015 at 22:03
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The other answers don't seem to explain that there are different (and conflicting) recommendations about the way to punctuate a list, which would seem to indicate that it is a misunderstanding to talk about the correct way.

Grammar.CCC.com recommends that you use exactly the style of your example:

If the explanatory statement coming after a colon consists of more than one sentence, begin the independent clause immediately after the colon with a capital letter [and punctuate following main clauses normally]:

There were two reasons for a drop in attendance at NBA games this season: First, there was no superstar to take the place of Michael Jordan. Second, fans were disillusioned about the misbehavior of several prominent players.

But I'm not saying that this is any more 'correct' than any of the other recommended variants (though it's the style I'd use).

Beware those saying 'this is the way you must do it' (but obey them if they're paying you or marking your final exams).

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  • Actually, I used that exact source to support my statements (see the comments).
    – Mike
    Commented Mar 28, 2015 at 22:44
  • Why didn't you use it to give a fuller answer?
    – Edwin Ashworth
    Commented Mar 28, 2015 at 22:49
  • Because the original question asked how to present a list within a paragraph, which I answered. When the OP inquired about punctuation rules in the comments, I expanded accordingly.
    – Mike
    Commented Mar 28, 2015 at 23:05
  • 'What is the correct way to introduce and write a list?' seems pretty general.
    – Edwin Ashworth
    Commented Mar 28, 2015 at 23:16

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