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
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 ;-)