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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[] and

[][][]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:-







[][]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.



Happy puzzle decoding.


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