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Hoverdia
Eighteen, which is represented by a standard
board game
of
8x8
boxes, is not just the
placement of numbers but
also involves additions and subtractions
for
brain
training at
any
age and
without any
language
barrier.
It
is
actually
an
Addictive
Brain
Game
that
involves
both
logical
thinking
and
arithmetic
solving. It
is
best
suitable
for exercising
not
only
the
left
brain,
but
the
right
brain
as
well.
This is a
non-violence
puzzle
game
which
is appropriate
for
educational
purposes
as
well
as
for
family
game.
It is not a rigid or difficult
puzzle game. It is
quite
easy
and fun
as there
are
many
alternatives
in
decoding
the
entire
puzzle. "There's always an opportunity, if there is an alternative" quoted by the Hovedia Puzzle editor. The
name of Hoverdia was derived from
the first two or
three
letters of HOrizontal,
VERtical and
DIAgonal. And Eighteen is one of the two rules in this
puzzle.
 There are two game rules for completing the
entire Hoverdia
Eighteen puzzle which
consists of 64
boxes
(8x8 boxes).
The main
puzzle is best
represented by 8 long horizontal blocks and 8
long
vertical blocks.
Each block
consists of
8
small
boxes, which
give a
total
of
64
boxes.
There are two rules: RULE
ONE and
RULE
TWO in decoding
the
puzzle
and
it
may
be
applied
interchangeably.
Besides these, there are two
more HINTS,
as
an
added
advantage
for assisting the
player to
decode
the
entire
puzzle.
The pre-set numbers in the Hoverdia
Eighteen
puzzle
are
not
always
in
sequence
either by
ascending
order from 1
to 8
or by
descending
order
from 8
to 1
but
will be usually
jumbled
up
or
in
random
order.
It really doesn't matter how or
which way the player to start with -
the
most
importance
is
when the
player complete
the
entire
puzzle
that
is
in
compliance
with
the
Hoverdia
Eighteen's
Rules.
The aim of this puzzle game is that each
long block must contain all
the numbers from 1 to 8 inclusively; and
the main puzzle is
also represented by 4
Quadrants of 4x4 short
blocks whereby
each
short block
with 4
boxes,
when filled-up
with
numbers, must be added
up
to an exact sum of
18
not
only
horizontally
and
vertically;
but
diagonally
as
well.
The
characteristic
of
all
the
8 long
horizontal
blocks
and 8
vertical
blocks
together
with the
4
quadrants,
where
each
quadrant
consists of 4
short
horizontal
blocks
and 4
short
vertical
blocks,
in
which
some
numbers
have
been
filled
up
in
advance,
are
the
essential
building
blocks
of
HOVERDIA
EIGHTEEN.
  All 8
long
horizontal
blocks
and
8
long
vertical
blocks,
which
have
8
boxes
in
each
block,
each
box
must
contain
one
of
the
numbers
ranging
from
1
to
8
inclusively
without
repeating
any
number
thereof.
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.
  Each quadrant (4x4 boxes) shall not
contain more
than
2 sets
of
numbers
from
1
to
8
exclusively.
Each number, from a set of numbers 1 to
8
exclusively,
cannot
appear
more
than
twice
within
any
of
the
four
quadrants.
For
any
of
the
4
quadrants
(4x4
boxes),
there
should
be
only
one
pair
of
number
from
1
to
8.
For
example,
if
there
are
already
placed
with double
8,
then
the
third
8
cannot
be
placed
therein
even
through
it
is
in
compliance
with
Rule
Two as
it would
affect
the
opposite
quadrant
when Rule
One
comes
in.
  Same
number may
be repeated
twice within the same
diagonal
block in
any
of
the
4
quadrants
(4x4
boxes).
Repeating numbers can only apply
to diagonal
block and not
in any
other
block.
This
is
possible
becuase
the
repeating
numbers
residing
not
only on
separate
vertical
blocks
but
also
on
separate
horizontal
blocks
as
well.
 A list of all possible
combinations of having
double numbers or
repeating
numbers
which is exactly
added
up
to an exact sum
of
18.
This peculiar situation can only be happened
and applicable to
Diagonal
block.
For any beginner, it may have to go through all the
detailed
explanations
and perhaps have to
memorize initially
some
of the possible
combinations of numbers
BUT for an advanced
player, just
remember
the 8 sets of
combination would do the
trick.
It is for illustration purposes only. The ultimate aim is to
master it and to get all these
into the brain
without having
to
refer to it, in any
form.
IT IS ALL ABOUT MENTAL
CALCULATION. ALWAYS START WITH RULE TWO.
Happy puzzle decoding.
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