Uber- Ultra- and Hyper-Gogen Puzzle Books

250 graded UberGogen and UltraGogen puzzles in each book.
Click on the links below.

The UberGogen and UltraGogen puzzles in these books go from: the easiest you can find on this site on a Monday that will take you ten minutes to do; to the hardest ones that you get on a Sunday - to give you an idea, the one below-left isn't the hardest I have done and it took me about an hour. Try today's puzzle by clicking Here.

For the uninitiated, a Gogen puzzle has a 5x5 array of cells within which the letters A-Y are placed. Some of those letter positions are given to you as cells that are filled in for you. To find the rest of them, you are given word clues that show you where the missing letters go. Usually, there are nine cells given away and the word clues provide all of the letters in the words. With an UberGogen, not all of the letters are given in the clues. With the UltraGogen, fewer clue cells are filled in for you but all of the letters are in the word clues. There is a tutorial here for you, explaining the subject in more detail.

Each book consists of 250 puzzles that are all new, never been published - 125 Uber-Gogen puzzles and 125 Ultra-Gogen puzzles - along with the answers at the back and, as you would expect, they increase in difficulty as you work your way through them. You can see on the 'Look inside' feature on Amazon's website, what the puzzles look like - they are printed in a 5½"x8½" which is a bit narrower than DIN A5 paperback format on off-white paper so they are easy on the eye, a good, practical size and will still fit in your pocket - take it with you anywhere and get stuck into it whenever you want. There is literally hundreds of hours' worth of entertainment in each book.

So, whether you are a hardened puzzle junkie, someone who wants to become one or you need to find a gift for somebody that is one, this is the only place you will find them.

Currently, there are four books (a total of 1,000 puzzles) and you can go to each book's Amazon page by clicking on the links below. Amazon will send the books you order to any address you specify (and wrap them as gifts if you want them to)

How do I know that all of the puzzles are new? Well, I don't know with absolute certainty but it's a guess with pretty good odds. For the Uber- and Ultra-Gogen 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 (that would give a sea-level rise of around 58m or 190 feet drowning Nottingham and Manchester but giving rise to the new Port of Leicester); or, 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. 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 Hyper-Gogen 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... 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 just one atom thick would stretch for 3,317,064,512,161,309,687m and would take light 350 years to travel the length. Around 230,998,737 times more combinations than Rubik's Cube (see above). A Hyper-Gogen book with 250 Hyper-Gogen puzzles (as well as 25 each of Uber-Gogen and Ultra-Gogen puzzles to get you warmed up) should be out in the next couple of weeks so watch this space and in the mean time, get some practice in ;-) Have Fun.

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Copyright ©2019 Paul Alan Grosse.