afterward, afterword...

56 out of 76

57 out of 76

58 out of 76

   73601 x    98376 = 7240571976

   incas x    tonic = idealistic

42U609783 71 411439705 98 46838M76 1U66411

education is essential to economic success

59 out of 76

60 out of 76

...

This is the  solution as in my previous posting. I got there in part through a generous hint by Ady. This is the tale of my steps and missteps.

 

(I had to solve the puzzle, because, how can you put down a puzzle that has the word "pisco" in it? More, below.)

First, I had the strong suspicion that "c" was in fact coded from the 10 letter word "idealistic". This is the longest word in the sentence and it also seemed forced into the sentence: if you know about the Incas, you know they were anything but idealistic. (More on this below, too). 

Yes, there were eight 5-letter words that could multiply together to make a 10-letter word (28 possible pairs), but there were also thirteen 2,3,4,7 & 8 letter words offered as well. I wrote a code that would check all combinations of all factor pairs of all numbers between 0123456789 and 9876543210 (there are a lot!). Before coding, I checked that my INTEGER types could handle numbers with 10 digits. But I did my check sloppily. While some ten digit numbers can be represented by 8 4-bit bytes (max = +/- 2^31), the magnitude of the answer c, 7.24 10^10 needs more bits (like 37). So, without knowing it, I was getting integer overflow, with the the sign bit flipping on, and incomplete results. In the process, I erroneously excluded "idealistic" for not having the needed factors. I went on to the next longest word "beverage" and found a unique solution (posted). However, the solution didn't fit the end phrase. So, I started exploring 7-letter words (there are 3). I was saved by Ady's hint and then knew the answer was 10 letters,  and I had to have a bug in the original program. So, I went back to the 10-letter program and found it. I recast all integers there as the 64-bit kind. The program then ran much slower but right. It got the unique posted result (with about 20 minutes of execution time.) The program here. 

Why do I say the Inca were not idealists? 1) They were politically crafty: they infiltrated and subjugated indigenous groups: offering them them prosperity but also taking possession of their religious idols. The Incas removed their idols, reinstalling and enshrining them in Cusco. This made pilgrimages to Cusco, the Inca capital, necessary for the people's worship and solidified the government control. 2) they were tax hounds. They taxed everyone and recorded all taxes on their quipus (string abacuses). When a community was too poor to give back any real wealth, like in the Lake Titicaca area, the Inca leaders instead demanded a specific number of fleas, to be given as token taxes. (Inca bugs, as advertised). 3) They were political fakers, pretending to communicate with the Sun God, with each leader instructing his son, the heir, to carry on with the charade. 4) They were autocrats, suffering internecine warring, which allowed the Pizarro brothers to quickly take over the pyramidal government from the top, garroting Atahualpa and destroying the empire. It helped that the Incas were highly outmatched in most tools of war.

As for the recipe for pisco sours, I do prefer this to the popular chicha drink. Even better is the poncho con leche (made in Paracas, e.g.) made from pisco, raw eggs, warm milk and nutmeg.