Uber- Ultra and Hyper-Gogen Puzzles - About page. Grosse Puzzles

UberGogen UltraGogen HyperGogen and HyperGogen+ Puzzles

Gogens are a generic word puzzle (the name 'Gogen' is not trademarked) that uses a 5x5 grid that is marked with some letters and, using the words provided, the solver has to place the remaining letters on the grid. You might have seen them in some newspapers but the puzzles that I produce here are a little more difficult to solve. Just like the Sudoku and Kakuro puzzles, every day, I put brand new, unique, Uber-Gogen, Ultra- and Hyper-Gogen puzzles on this web site for you to print out and solve and it doesn't cost you a thing. Also, like the Kakuro and Quadrata puzzles, they get harder as the week goes on.

If, however, you would like puzzle books containing the variants of Gogen puzzles, either for yourself or as a gift for somebody Click Here to go to the puzzle books page. Books contain from 100 to 366 brand new puzzles and make an ideal present.

The UberGogen puzzle uses the standard corner, face-centre and body centre clues but as the week goes on, the word list includes fewer of them. On the Monday, there can upto one of the letters missing from the word list - you might find, say, that the letter 'W' isn't included in the word list and it might be that its position is already defined as one of the declared letters although it might be that it is not. As the week progresses, the chance of an increasing number of missing declarations manifests itself until, on a Sunday, there can be as many as seven missing. The puzzle is still soluble but you have fewer clues as to where things go.

The UltraGogen displays fewer declared letters as the week progresses, working its way through a number of patters, starting at eight declarations and finishing the week declaring just two or three letters on a Sunday although in the case of the UltraGogen, all of the letters in the puzzle are always in the word clues.

The HyperGogen throws away all that is familiar, apart from, perhaps the fact that you are using letters of the alphabet. There, the similarity ends. Not all of the declared letters have to be in the clue words and not all of the 25 letters have to be found in the clue words. As though that was not enough, the clue words can have letters appearing more than once, they are not limited to words three or more letters and the clue words consist only of the letter bonds without any similarity to words in any language other than by accident.

The HyperGogen+ is basically a HyperGogen puzzle except that there is a word hidden in there of at least nine letters long. You don't know what it is, there are no clues to its identity, you don't know where it starts or ends or the path it takes. In fact, you might identify the word as starting with un- or de- or ending with -s or similar where the word placed there by the program did not, thus identifying a longer version of the word and beating the program. All that you know about the word is that it has no repeating letters.

The GoldenGogen as far as the puzzle solver is concerned is essentially a HyperGogen+ but it is Golden because of the way that it is formed. The GoldenGogen is designed by hand so in theory, it has not got such a high level of entropy as the HyperGogen, however, the way that the puzzles pseudo words join up the network make these puzzles both fiendish to do as well as a pleasure. Being designed by hand, you might look at a GoldenGogen puzzle and think that there are a lot of clue cells on the board whereas it might be that only one of them actually links up in the clues. Also, the number of clue cells can range from nine down to just one.

	Normal	Uber	Ultra	Hyper	Hyper+	Golden
	Gogen Type
Located clue letters	9	9	2-8	2-6	2-6	1-9
All 25 letters found in word clues	Yes	No	Yes	No	No	No
All word clues longer than two letters	Yes	Yes	Yes	No	No	No
Only Latin letters used	Yes	Yes	Yes	Yes	Yes	Yes
All 25 letters linked	Yes	No	Yes	No	No	No
Real words used as clues	Yes	Yes	Yes	No	No	No
Letter used only once in each clue word	Yes	Yes	Yes	No	No	No
Time to do puzzle in minutes	5-10	10-30	20-90	20-150	20-180	10-240
Hidden long word in puzzle	No	No	No	No	Yes	Yes

The number of puzzle possibilities is an interesting one - it is such a high number that the chance of producing two puzzles the same at random is extremely remote.

For the UberGogen and UltraGogen Puzzles: With a dozen layouts used and eliminating mirrors and rotations, that makes 23,266,815,064,996,478,976,000,000 combinations which is about the same as:

The number of millimetres from Earth to the Andromeda galaxy;
Roughly the number of water molecules in two 350ml cups of coffee;
If you were able to stretch that many gold atoms to make a filament that was only one atom thick, it would be 3,955,358,561,049km long which would take light 5 months to travel;
The number of cubic millimetres (microlitres) of ice in the Antarctic ice cap (if it melted, it would produce a sea-level rise of around 58m or 190 feet drowning Nottingham and Manchester but giving rise to the new Port of Leicester);
The number of wrong lottery combinations in the UK Natonal Lottery if you had to choose 29 correct balls from a total of 102 instead of choosing 6 correct balls from 59 and that is up from the 6 correct balls from 49 where the half hour program where you watched them perform the draw gave rise to a situation were you stood a greater chance of dying of a heart attack whilst watching the program than you did of winning it; or,
It has 537,936 times more combinations than Rubik's Cube (which has 43,252,003,274,489,856,000 combinations) so one might argue that it is that many times harder - it certainly takes me longer to do any of the Gogen puzzles on this site than it does for me to solve a Rubik's Cube.

For HyperGogen and HyperGogen+ Puzzles There are between two and five clue-cells in each puzzle and they are not allowed to be next to each other horzontally, vertically or diagonaly. That means for a puzzle with two clue-cells, there are 25 positions for the first cell and then: if the first is is a corner cell, 21 cells; if it is a side, 19 cells; and, if it is in the middle nine, 16. Add them all up and you get 456 but there are factorial two ways of getting them so divide by two and you get 228. For three, you get a further 964; for four you get 1,987; and for 5, you get another 978 making a total of 5,153. (for the morbidy curious, for 6 you get 978 and 7 you get 242, for 8 you would get 9 and for 9, there is just one.) So, multiply that sum by factorial 25 (the number of letter combinations and then divide by eight for rotations and reflections, and you get 9,991,158,169,160,571,346,944,000,000 different layouts (or roughly a 1 with 28 zeros after it)) which is...

The length of the Pisces-Cetus Galaxy Supercluster Complex in millimetres. It is a filament of galaxies that contains our Milky Way galaxy;
The number of cubic millimetres (microlitres) of water on seven planet Earths;
Just short of the number of molecules in three hundred litres of water (just over 10 cubic feet);
Half as much again as the weight of the Earth in grammes;
A gold thread of that many atoms but just one atom thick would stretch for 3,317,064,512,161,309,687m and would take light 350 years to travel the length;
The number of wrong lottery combinations in the UK Natonal Lottery if you had to choose 29 correct balls from a total of 122 (see above); or,
Around 230,998,737 times more combinations than Rubik's Cube (see above).

The process of making a dictionary for Gogen puzzles is an interesting one. First of all, you start off with a word list - you can source these online and in the case of mine, it started off with 117969 words in it.

Unlike text from books or speech, these words are all different and can not only be found in everyday speech but also the more esoteric words that you find in word games.

The rules for the standard Gogen, the UberGogen and UltraGogen are that:

Words have to be at least three letters long, so out go 85 words, leaving 117,884 in all.
Next, we want to get rid of letters with a 'Z' so out go another 3,664 words, leaving 114,220.
Next to go are words that contain more than one instance of any letter such as the 'N' in 'instance' and so on so out go a further 83,725 words, leaving us with 30,495 words.
Finally, we don't want any profanity (although you can guarantee that somebody, somewhere on the planet will be offended by some random word, no matter what it actually means) so out go another 85 words, leaving a grand total of 29,332 words.

Remembering that we have started off with a list of words that are all different so the letter frequency distribution is going to be affected slightly by that, of all of the above processes, the main impact on the proportion of letters (ignoring the letter 'Z') is going to be the removal of words that have multiple instances of letters - removing the single word 'letter' takes out two 'E's and two 'T's, for example.

The list of letters in normal writing where words are repeated is	etaoi nshrd lcumw fgypb vkjxq z
The letter frequency list for all words appearing once is...	esiar ntold cugpm hbyfk vwxjq
...and for the Gogen word list, it is	esair onltu dcgmp hbykf wvxjq.

Below are two tables of letters in the lists of words. Words with two letters the same in them are therefore included in the full word list but eliminated from the other list so letters that have a tendancy to appear more than once in a word will be depleated in the Gogen table. The table on the right is a combination of the two, showing the letter to letter ratios between the two dictionaries.

Full Word List
(117,969 words, 927,797 letters)

Let

Frequency

109,807

89,259

79,534

71,086

66,809

62,075

58,627

56,667

48,428

35,623

35,385

32,206

28,653

26,758

25,584

20,969

18,603

14,028

13,105

10,004

9,444

8,792

2,801

1,878

1,672

Gogen List
(29,332 words, 190,163 letters)

Let

Frequency

17,839

15,591

14,149

15,243

13,473

11,430

10,617

11,792

10,620

7,826

7,634

8,503

6,119

5,866

5,919

5,741

4,523

4,503

2,855

3,324

1,975

2,804

747

637

433

G
E
N
E
R
A
L

D
I
C
T
I
O
N
A
R
Y

GOGEN DICTIONARY

Below are three tables:

The first shows the distributions of letters in the clue words. YOu can see the the letters lower down in the list appear more frequently than in the two tables above - this is because they have been chosen to make actual puzzles so their frequency will be higher.
The second shows the letter bond frequencies in the word lists - the number of other letters a particular letter is joined to in the clues. You can see that there is little difference between the Uber- and Ultra-Gogen puzzle words although one letter that does stand out as being less frequent is the letter 'S'. This is most likely to the fact that it finishes off words and is therefore only joined to one letter in those instances. The Hyper-Gogen letter bonds show that the distribution is effectively flat as there are no real words in there other than by accident.
The last table shows the frequency of letters in each puzzle where a given letter not only is absent from the clue words but also from the given letters - in other words, it is the missing letter that you have to work out using a process of elimination. Only the Uber- and the Hyper-Gogen puzzles do this and you can see that the Hyper-Gogen puzzles show no particular preference as they are random and not related to any particular words. The two distributions in the Uber-Gogen puzzles show the inverse of the other two sets of tables and this is probably down to those letters under-representation in the word list making it easier to eliminate that letter with the removal of a single word during the formation process in the puzzle algorithm.

Again, these puzzles are produced by my computer, only for this site, using a computer program that I wrote myself in Perl. The solver part of my program uses logic only, it does not use brute-force and as a result of this, you will be able to solve them using just logic and yes, the ones with only two or three anchor-letter clues in them are possible to do - I've done them myself.