Free Tickets to Rio!

Question

I got an email from one of my friends in Brazil today morning:

"Free tickets to the Rio Olympics if you can solve all these! Good luck!!"

Clues:

$\longleftarrow 8\;\bar{\uparrow} $
$10 n=$
$\text{log}_{\boxed{b}}a+\bigg\{x\in V\bigg| \;||x||<r^2\bigg\}$
Darts, fencing, baseball, and skeet-shooting without golf, skateboarding and table tennis
I, on a strange game
Foul herb; no return
Proportion led by acid dissociation constant
Each stilt is broken
$\begin{cases}y=x^{20x},\\ y=x^{16},\\ xy^2+x^2-2x=0, \\ x^2+y^2=1.\end{cases}$
When you line up and quarrel continuously
Hello, your majesty!
$f(\infty)^t+\bigg\{x\in V\bigg| \;||x||<r^2\bigg\}$

Grid:

I really have no idea what this is all about, except that I have a feeling these are all sports related. Can you help me out by solving these for me?

Note:

The clues above are not necessarily standard cryptic-clues. For example, almost none of them includes definitions.
Exactly half of them are related to non-Rio sports.

4

Got my mind blown by 4! – Christoph Aug 09 '16 at 07:07
1

one of the best puzzle .. – Amruth A Aug 09 '16 at 10:04

Christoph · Accepted Answer · 2016-08-09T07:22:52.587

22

1

Weightlifting - arrow pointing West + eight + a symbol for lifting

2

Tennis - ten + n + is

3

Baseball - b is the base of the logarithm + the equation for a ball

4

Chess - remove the letters of golf, skateboarding and tabletennis from the letters of darts, fencing, baseball and skeetshooting. The remaining letters can be rearranged to form the word chess.

5

Oina - anagram of "I, on a", and surely in a way strange, as I've never heared about it

6

Badminton - bad mint + 'no' reversed

7

Karate - Ka is the acid dissociation constant + rate

8

Athletics - the clue is an anagram (Credit goes to @RosieF)

9

Judo - plot the equations to get the shapes of the letters

10

Rowing (Credit goes to @RosieF)

11

Hiking - Hi, king!

12

Football - f + $\infty$ + t + the equation for a ball

The phrase is

Welcome to Rio

edited Aug 09 '16 at 07:22

answered Aug 09 '16 at 06:47

Christoph

3,881
20
29

I can see the phrase already from these letters. rot13(jrypbzrgbevb) – f'' Aug 09 '16 at 06:51
I'd have never come up with 5 without guessing the phrase and searching for sports starting with this letter... ;) – Christoph Aug 09 '16 at 06:55
Common Chris waiting for final answer.. – Ram Visagan Aug 09 '16 at 07:21
There you go! Credit for 8 and 10 goes to @RosieF! – Christoph Aug 09 '16 at 07:24
1

@Christoph. What? you've never heard of Oina? Tsk Tsk... https://en.wikipedia.org/wiki/Oin%C4%83. Just for the record....I'm from Romania :D – Marius Aug 16 '16 at 13:46

score 7 · Answer 2 · edited Aug 09 '16 at 07:25

7

8.

Athletics (the clue is an anagram)

10.

Rowing

4.

Chess (remove the letters in the latter list from the letters in the former list)

edited Aug 09 '16 at 07:25

Ram Visagan

404
1
4
20

answered Aug 09 '16 at 06:59

Rosie F

8,621
2
18
50

Free Tickets to Rio!

Clues:

Grid:

Note:

2 Answers2