What are the next two numbers in this series and why?
3-3-5-4-4-3-5-5-4-3--
Clue: they are the same number.
I don’t particularly like mathematical puzzles but this one is unusual. I invented it while playing games on vacation.
6 - 6
and the next one, BTW, is 8
Very well done Twickster.
I’ll venture 3&3. The reason being that it’s always two identical numbers followed by a single number followed by a pair.
a-b-c-d-e–f-g-h–i--j-k-l
3-3-5-4-4-3-5-5-4-3--
a&b are a pair
c is single
d&e are a pair
f is single
g&h are a pair
i is single
J&*would thusly be a pair so k would have to be identical to J making K 3
l is a single which is a incidental triple.
At least, that’s my rationale.
but then back to 7 - 7 , usually Dyslexia isn’t a problem for math games.
Here’s another some might not know
Find the anagram of ONE PLUS TWELVE that is also 13.
D’oh!:smack: What’s the rationale for the 8-8 though?
ELEVEN PLUS TWO
Grrr, I meant 6-6.
Check my profile – I’m a trained professional. 
Spot on Ex Machina
If in Quebec you might try
2-4-5-6-4-3-4-4--
in which case the tow missing are not the same.
Cool, the light over my head has a dimmer apparently, I get the 6-6 now.
A&B, then C, D=A+1&E=B+1, then F, G=D+1&H=E+1
Interesting Stpauler.
But if you want to know the secret here is a clue. One number in the original series is unique for a special reason. The unique number is the first 4.
Speaking of anagrams, here is another puzzle I made up. Try to think of four letters which can be rearranged to form six different words.
OPTS
POST
POTS
SPOT
STOP
TOPS
Outstanding Gyrate!
Shouldn’t that be
OPTS
POTS
POST
TOPS
SPOT
STOP
or am I missing something (quite probably)
Just as I post, I spot your using alphabetic rather than first word order.
And would LOoP be allowed?
LOoP
LoOP
POoL
PoOL
PoLO
POLo
Since the words, and not just the individual letters, must be different, I would vote ‘no’.
ores
o’ers
Eros
rose
roes
sore
or for three letters (without using acronyms/abbreviations)
ate
eat
eta (Greek Letter)
tae (From Tae Kwon Do, pushing it 
)
tea
There’s also:
ARTS
RATS
STAR
TARS
TSAR
and, obscurely,
SART (n. An assart, or clearing. [Obs.])
See? Ya learn something new every day.