A Quintumble grid consists of 25 letters laid out in 5 rows and 5 columns. Each letter in the 1st column can be paired with 5 different letters from the 2nd column, which in turn can be combined with 5 different letters from the 3rd column, and so on. Thus, there are 5 x 5 x 5 x 5 x 5 = 55 = 3,125 possible ways to combine the letters.
For each of the 3,125 combinations, there are 45 = 1,024 ways to combine the remaining 20 letters. And for each 2-combination pair, there are 35 = 243 ways to combine the remaining 15 letters...and so on. Thus, there are 55 x 45 x 35 x 25 x 15 = 3,125 x 1,024 x 243 x 32 x 1 = 24,883,200,000 different combinations of five 5-letter combinations. That’s almost 25 billion possibilities!
But don’t let this number intimidate you. Like any good puzzle-solver, you can use your keen eye for pattern recognition (employing some clever tips & strategies) to drastically reduce the number of actual possible combinations.
Most Quintumble puzzles result in only about 40 to 80 words among the 3,125 possible combinations. Each of these words can be paired with just some other words, which is only possible if they don’t share a letter in the same position.
For every 2-word pair, there will be a smaller subset that can be combined with a 3rd word and an even smaller subset that is possible with four words
Finally, for all the 4-word combinations, there is just one that takes you all the way. Out of nearly 25 billion possibilites, there is only 1 unique combination of 5 words that can be made together. How about that!