Why does Yomi relate 3661 with "Samurai"? In the last episode of Azumanga Daioh, Yomi relates 3661 with samurai word. 


I know is a mnemonic technique to remember things, so things should be something like:

3 ~&gt; sa ~&gt; san
6 ~&gt; mu ~&gt; ??? (maybe shape of hiragana? む )
6 ~&gt; ra ~&gt; ...roku??
1 ~&gt; i  ~&gt; ichi


But I couldn't guess at all why relates 6 with both mu and ra. Any idea?
Japanese speakers may remember numbers by taking the prominent syllable from how they read numbers (語呂合わせ goroawase). There are more than one way on how to count: one that descended from Old Japanese (大和言葉 Yamato kotoba) and one borrowed from Chinese (漢語 kango). In the order of Yamato / Kango:


ひとつ hitotsu / いち ichi
ふたつ futatsu / に ni
みっつ mittsu / さん san
よっつ yottsu / し shi
いつつ itsutsu / ご go
むっつ muttsu / ろく roku
ななつ nanatsu / しち shichi
やっつ yattsu / はち hachi
ここのつ kokonotsu / きゅう kyū or く ku
とお tō / じゅう jyū


and so forth. Therefore, a syllable that corresponds to 3 can be either み mi, さ sa, or ざ za (the last being the voiced variation of sa).

For 3661,


3 = sa from san
6 = mu from muttsu
1 = i from ichi


The second 6 requires explanation. Notice that in the list above, "ra" does not appear. In fact, most of the syllables do not have a direct corresponding number, given that there are 48 basic syllables (plus 25 voiced variants and 21 digraphs). To force any given syllable into a number, people use various techniques. 


Use English. つ tsu = 2, せ se = 7, え e = 8
Use modern Chinese. す su = 4 (written sì in pinyin but sounds like su), り ri = liù = 6
Swap vowels. This is what happened to the second 6 in 3661. Of all the syllables in the ra-line (ra, ri, ru, re, ro), only re (0 from rei) and ro (6 from roku) are defined. The Chinese technique also suggests 6 for ri. Therefore, 6 may be extended to ra and ru also. (The same thing happens in the ko/go-line where 5 fills in for ka/ga and ke/ge; and in the ma-line where 6 fills in for me and mo.)


An example of this extended list can be found at http://www2u.biglobe.ne.jp/~b-jack/kouza/s-3.html 

With these techniques in play, people might remember the first 30 digits of pi as follows:

San ishi ikoku ni mukau. Sango yaku naku, 
3 . 1 4  15 9  2  6 5    3  5  8 9  7 9
Obstetrician goes to a foreign country. No misfortune after birth,

sanpu miyashiro ni. Mushi sanzan yami ni naku.
3  6  3 8 4  6  2   6 4   3  3   8 3  2  7 9
the new mother heads to a shrine. Insects chirp in the darkness severely.