Riddles, brain puzzles and mathematical problems

[BAndrew]

4^4 + (4*4)^4 --> allowed

But there are four 4s and five here?

Ooops yeah, sorry. In my hurry to show that you can't use another digit I forgot about that. Thanks. I corrected it.

[Froge]

Spoiler below!

(2 + 2)! = 24
3^3 - 3 = 24
4*4 + 4 + 4 = 24
((5 - 5) * 5 + 5)! / 5 = 24
6 - 6 + 6 + 6 + 6 + 6 = 24

will update post as i find moar

[BAndrew]

Alright, good job so far!

Please use spoilers because maybe others want to solve it.

write

(spoiler) your text here (/spoiler)
but instead of ( and ) use [ and ] respectively

[BAndrew]

New short riddle. Find the next number in the sequence.

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, ?

Explain your reasoning. There might be many possible answers.

[7heDubz]

Noctemwolf found this one! (my brother =P)

885.
Because...

Spoiler below!

starting with 2 you add one (2 to 3), then multiply by 1 (3 to 3), then add 2 (3 to 5) then multiply by 2 (5 to 10) so on so forth. reaching 177 you multiply it by 5 and reach 885.

[BAndrew]

Great thinking Noctemwolf!

[PutraenusAlivius]

Based on the short number riddle.

1, 2, 4, 7, 11, 16, 26, 37, 49, 62, 76, 91, ?

Next number?
NOTE: It's just simple addition.

[BAndrew]

Based on the short number riddle.

1, 2, 4, 7, 11, 16, 26, 37, 49, 62, 76, 91, ?

Next number?
NOTE: It's just simple addition.

Spoiler below!

111
+1+2+3+4+5+10+... continue until you reach 15 and then go to 20 and so on. In other words you skip the numbers that end with 6,7,8 and 9

[PutraenusAlivius]

Based on the short number riddle.

1, 2, 4, 7, 11, 16, 26, 37, 49, 62, 76, 91, ?

Next number?
NOTE: It's just simple addition.

Spoiler below!

111
+1+2+3+4+5+10+... continue until you reach 15 and then go to 20 and so on. In other words you skip the numbers that end with 6,7,8 and 9

Nice work man!

[BAndrew]

Let q1,q2,q3,...qn natural numbers.
(Set of natural numbers is N={1,2,3,...})

Given that:

• q1/q2 = k
  
• q1/q2 = q2/q3 = ... = qn-1/qn
  

Find q1/qn


NOTE: Only basic algebra is required. Nothing special.
NOTE 2: The solution is really, really short, but elegant.