# Missing digits

• June 1st 2009, 06:45 AM
alana
Missing digits
Hello everybody,

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

12xy
11121x1y
3112111x111y
?

(Hi)
• June 1st 2009, 07:26 AM
Soroban
Hello, alana!

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

Quote:

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

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

Each row describes the contents of the row above it.

The first row is: . $12xy$

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

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

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

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

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

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

• June 1st 2009, 07:55 AM
alana
:)
Dear Soroban (Bow),

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!

(Happy)