In a far other universe, my little sister was trapped in a cave. Surprisingly for humans, in this universe, all caves are electronic. This electronic cave had nothing but 5 buttons, two little screens, one red and one blue, a numeric keypad, and the most brought to light, this little message:
Press the wrong button and that'll be your last action, press the right button and leave this cave.
The red little screen output the number
11. The blue output
The five buttons had 5 different colors. My sister had always been an expert for colors (as well as having a PhD in colors (what a strange universe...)) and she could perfectly remember those:
What my sister did
To escape, my sister first pressed her favourite number into the numeric keypad :
Immediately, the blue screen started blinking. And 5 seconds after, it output the letter
y. Simultaneously, the red little screen changed and output
10. At that moment, she understood she had to wrote down to a little piece of paper she had:
That's not here for nothing
She then tried
10 but those four numbers didn't changed the blue output and more stressful than anything, after that the red screen output
I was born the...
03 and thankfully the blue showed:
17: v 3: u
The red showed
Our cat was born the...
25: s 11: p
Father was born the...
She finally tried
29: q 77: m
How did she survive?
Alright, that's been four days that this puzzle is still unbreakable :p. Here is the first Hint I can give you:
You probably found it, this puzzle is to find a certain $f$, which takes in input a number and returns one of the $26$ letters of the alphabet. This hint is to give some facts on $f$ and its link to this puzzle.
1. You also probably know that but the aim of this puzzle is to find $f(19)$, $f(8)$, $f(7)$ and $f(10)$.
2. $f$ is defined on any positive natural number, it is not defined on zero, it is not defined on negative numbers. It could be possible to define it by being treacherous but I haven't done it and that's not necessary for the puzzle. Plus there is no minus symbol in the numeric keypad 😊!
As it's defined on positive numbers, here is a list of its values:
$f(1) = p$
$f(2) = y$
$f(3) = u$
$f(4) = v$
$f(5) = k$
$f(6) = d$
$f(7) = ?$
$f(8) = ?$
$f(9) = w$
$f(10) = ?$
$f(11) = p$
$f(42) = e$
Please specify in your answer whether you solved the puzzle with or without hint 2.a and hint 2.b
Hint 2.a 7 July 19
After being stuck for hours within this cave, my sister noticed that the ground was discreetly etched by the 26 letters of the alphabet. There was a mathematical symbol next to the 26 letters.
Hint 2.b 14 July 19
The mathematical symbol is $\%$.
Hint 3.a 17 July 19
Actually modulo operation is used once or twice, or isn't used, to encrypt each number. Another important operator used within the encryption is $+$, it's systematically used once. The latter could also have been etched to the ground!
Hint 3.b 17 July 19
Hint 2.a is as much important as Hint 2.b. The fact that the alphabet is etched is important.