Bartender's nightmare

Question

Turn the "before" picture into the "after" picture by pouring the ice cubes from one glass to another.

Before

After

Specifically:

• Start: There are three glasses. The first glass is a 5-capacity glass with the word ENJOY written downward on 5 ice cubes. The second glass is a 5-capacity glass which is empty. The third glass is a 4-capacity glass with the word THIS written downward on 4 ice cubes.
• Objective: Pour ice cubes from one glass to another until the first glass is empty and the word ENJOY is written downward in the second glass. The third glass should end as it started, with the word THIS written downward.
• Movement: A pour continues until either the donor glass is empty or the recipient glass is full, whichever happens first.
• Note: Letter order is reversed (upside-down) after pouring. I.e., if ABCD is poured, it will appear as DCBA in the recipient glass.

Answer 1

It can be in too many moves but it can be done.

Notation: To show a position I will display the glasses horizontally, with the bottom at the right. The three strings represent the glass content from top to bottom. Available empty space is represented by a -.

So we want to go from
ENJOY ----- THIS
to
----- ENJOY THIS

A sequence of moves is noted as number pairs, the source and destination glasses. For instance we could do the sequence 32 13 32:

ENJOY ----- THIS
ENJOY -SIHT ----
----Y -SIHT OJNE
----Y OSIHT -JNE

The solution involves a few steps.

Preparation:

First we free the 3rd glass with the move 32.
ENJOY ----- THIS
ENJOY -SIHT ----

If we manage to reverse the 'ENJOY' without disturbinb the 'SIHT', we can finish by transferring these to glasses 3 and 2 in the correct orientation.

First we define two move sequences:

Sequence A: 13 12 31 21:

ENJOY -SIHT ----
----Y -SIHT OJNE
----- YSIHT OJNE
-ENJO YSIHT ----
YENJO -SIHT ----

Sequence B: 13 32 31 21:

ENJOY -SIHT ----
----Y -SIHT OJNE
----Y OSIHT -JNE
-ENJY OSIHT ----
OENJY -SIHT ----

Sequence A rotates the 5 letters of the first glass. 'ENJOY' becomes 'YENJO'. Sequence B rotates only the first 4 letters of the first glass. 'ENJOY' becomes 'OENJY'. These two sequences can be combined to reverse the word 'ENJOY'.

Combination:

After the initial move, we execute the sequences: B B A B A B A A.

This affects the letter in the following way. Each line is the result of one sequence A or B.
ENJOY -SIHT ----
OENJY -SIHT ----
JOENY -SIHT ----
YJOEN -SIHT ----
EYJON -SIHT ----
NEYJO -SIHT ----
JNEYO -SIHT ----
OJNEY -SIHT ----
YOJNE -SIHT ----

Final:

As I said in the preparation, the final moves are just 23 12:

YOJNE -SIHT ----
YOJNE ----- THIS
----- ENJOY THIS

The number of moves is 1 for the preparation, 8x4 = 32 for the sequence of sequences, and 2 more final moves. That makes 35 moves in total. But I am pretty sure it can be done in fewer moves.

Update

A computer search returns solutions in 27 steps as 2012rcampion has found in the meantime.

It happens that one solution can be expressed using my A and B sequences.
If you do B A B A B B after the initial move, the effect is:

ENJOY -SIHT ----
OENJY -SIHT ----
YOENJ -SIHT ----
NYOEJ -SIHT ----
JNYOE -SIHT ----
OJNYE -SIHT ----
YOJNE -SIHT ----

Using this you get a solution with 1 + 6x4 + 2 = 27 moves.

Answer 2

The shortest solutions have:

27 steps

One example is the following:

E .   | . Y   | . Y   | Y .   | . .   | E .   | E .
N . T | . O T | S O . | S O . | . O H | N . H | N Y .
J . H | . J H | I J . | I J . | . J I | J . I | J S .
O . I | . N I | H N . | H N . | . N S | O . S | O I .
Y . S | . E S | T E . | T E . | T E Y | T . Y | T H .

. .   | . O   | . O   | . .   | H .   | H .   | . .
. Y O | . Y . | E Y . | E . I | E . I | E O . | . O J
. S J | . S J | N S . | N . S | N . S | N Y . | . Y N
. I N | . I N | J I . | J . Y | J . Y | J S . | . S E
T H E | T H E | T H . | T H O | T . O | T I . | T I H

. J   | . J   | . .   | I .   | I .   | . .   | . N
. O . | H O . | H . S | H . S | H J . | . J N | . J .
. Y N | E Y . | E . Y | E . Y | E O . | . O E | . O E
. S E | N S . | N . O | N . O | N Y . | . Y H | . Y H
T I H | T I . | T I J | T . J | T S . | T S I | T S I

. N   | . .   | S .   | S .   | . .   | . E   | . E
I J . | I . Y | I . Y | I N . | . N E | . N . | . N T
H O . | H . O | H . O | H J . | . J H | . J H | . J H
E Y . | E . J | E . J | E O . | . O I | . O I | . O I
T S . | T S N | T . N | T Y . | T Y S | T Y S | . Y S