1. ## Missing digits

Hello everybody,

i'd appreciate it very much if someone could help me solve this:

12xy
11121x1y
3112111x111y
?

2. Hello, alana!

This is a classic (very old) puzzle . . .

i'd appreciate it very much if someone could help me solve this:

. . $\displaystyle \begin{array}{c}12xy \\ 11121x1y \\ 3112111x111y \\ ? \end{array}$

Each row describes the contents of the row above it.

The first row is: .$\displaystyle 12xy$

It contains: .one 1, one 2, one $\displaystyle x$, one $\displaystyle y$.

The second row is: .$\displaystyle 1\;1,\quad 1\;2,\quad 1\;x,\quad 1\;y \qquad\Rightarrow\qquad 11121x1y$

The second row contains: .three 1's, one 2, one 1, one $\displaystyle x$, one 1, one $\displaystyle y$.

The third row is: .$\displaystyle 3\;1,\quad 1\;2,\quad 1\;1,\quad 1\;x,\quad 1\;1,\quad 1\;y \qquad\Rightarrow\qquad 3112111x111y$

The third row contains: .one 3, two 1's, one 2, three 1's, 1 $\displaystyle x$, three 1's, one $\displaystyle y$.

The fourth row is: .$\displaystyle 1\;3,\quad2\;1,\quad 1\;2,\quad 3\;1,\quad 1\;x,\quad 3\;1,\quad 1\;y \qquad\Rightarrow\qquad \boxed{132112311x311y}$

3. ## :)

Dear Soroban ,

thank u sooooo much for the solution and for replying that quickly. It was such a nice explanation. Best wishes and a kiss from Croatia!