There are 8 horizontal blocks and 8 vertical blocks with 8
boxes in each block which must contain all
from a set of
numbers [
**1**, **2**, **3**, **4**, **5**, **6**, **7**,
**8** ]
inclusively
without
repeating
any
number
thereof.

For
solving this
puzzle at
any
level
of difficulties, it
is advisable
to begin
with
any
Quadrant
(4x4)
which
is
deemed
easy
or
solvable by
applying
**Rule
Two**
before moving
onto another
adjacent
Quadrant
for
completing
all
the long
horizontal
blocks
and/or
long
vertical
blocks
in
order
to
comply
with
**Rule
One**
as
well.

In each of
the
4
quadrants,
all
4
short
horizontal
blocks
and
4
short
vertical
blocks
together
with
2
diagonal
blocks,
which
have
4
boxes
in
each
block,
must
be
added
up
to
the
sum
of
18
horizontally,
vertically
and
diagonally.

This
puzzle is
also
alternatively
represented by 4
Quadrants and
each
Quadrant
consists
of
4x4
boxes.

All
the
blocks in each
Quadrant,
which
consist of 4
boxes,
must
be
added
up
to an
exact
sum
of
**18**
horizontally,
vertically
and
diagonally.

This is
proven to be
the
**Best Initial
Approach**
in
solving
the
entire
puzzle in order to compliance with the
**Rule
Two **
by
starting from any
of
the
4
Quadrants
.

These **8 sets** of
combination are the **most
basic**
and yet
the **most
essential**
building block for this
Hoverdia
Eighteen's
decoding
technique.

Each set
combination is
listed in
ascending
order (from the smallest
value to
the largest
value among
the
four
numbers)
for
easy reference
purposes.

In actual fact, each of the 8 sets of combination
can be permuted into **24**
possibilities.

For example [ **1278** ], there are
24 possibilities
exclusively
: [
1278,
1287, 1728, 1782,
1827, 1872, 2178,
2187,
2718, 2781, 2817,
2871, 7128, 7182,
7218,
7281, 7812,
7821,
8127,
8172, 8217,
8271,
8712, 8721 ].

The
four
digits therein
are
remained the same but it
is just the
change
of its
positions.
The
same permutation
applies to the
remaining
7
combinations.

*This detailed number listing is an
***in-depth
analysis**
and
for
**your
better
understanding** only;
and you
are __not__
expected
to
memorize it
by
hard. Of all the Rules and
Hints of the HOVERDIA, the __most
importance__ is
**Rule
Two** as a lot of
emphasis
is
highlighted in
this
section.

A list of all possible combinations of numbers for **short
block**
which can be
added up
to an
exact
sum of
**18**
in **three**
different
situations where
a
particular
short
block
having ** one known number**,
** two known numbers**
and ** three known numbers**.

For **one
known number**
with three remaining
empty boxes,
it can
be
in
these
4
formats:-

**1**[][][],

[]**1**[][],

[][]**1**[] and

[][][]**1 **having
**1**
as the known number,
in this example.

By
referring to the table on the left
at **1**,
the four possible sets of
combinations
for the
three remaining empty
boxes are "**278**", "
**368**", "
**458**"
and "
**467**".

There are eight likely
formats
for
the **two
known**
**numbers** with two
remaining
empty
boxes:-

18[][],

[]18[],

[][]18,

1[][]8,

81[][],

[]81[],

[][]81 and

8[][]1 having 1 and 8 as the known numbers.

Refer to the Table on the left at **18**
for the
known numbers
**1** and
**8**,
the
three possible sets of combinations for
placing into the
two
remaining empty
boxes are "
**2 **&** 7"**, "
**3 **&** 6"** and
**"4 **&** 5"**.

Alternatively, you can look at **81** (last item
7 on the second
column) for the
known
numbers
**8** and
**1**, the
three possible sets of
combinations are the
same sets __as
before__ but the only
difference is
its
positions.

All these combinations should be added-up to an exact sum of 18
for a complete compliance with
**Rule
Two**.

The most straight forward situation is the **three known numbers** with single empty
box. It is just a matter of mental
calculation as it is also a **mind
game**. Firstly:
By adding up all
the three
known numbers,
a
sub-total will
be
obtained;
and finally:
By
subtracting
the resulting
sub-total
from
18,
the difference
thereof
would
be
the needed
number
for
the
single
empty
box.

If the three known numbers are
**1**, **6**
and
**7,** in
this
instance: Firstly,
by
adding
up
all
that
three
numbers,
you
would
get
14
as
a
sub-total.
Secondly,
by
subtracting
the resulting
sub-total
of
14
from 18, you
would
get 4.
Then,
the
single
empty
box
would
be
filled
in
with
**4
**as
the
combination
of
1,4,6
and
7
would
be
added
up
to
an
exact
sum
of
18
for
**Rule
Two**.