So I assume that 5, maybe 6 of you have been mulling over the riddle I posted last week. It was, without a doubt, devilishly difficult. If one were related slightly to Leonard of Quirm (Terry Pratchett reference, anyone?) you could easily say it was Arch-Demonically difficult. f=If you missed last weeks post about the riddle and want to have a look before seeing the answer, follow the link here: To Boldly Go: A Star Trek Riddle.
So I’m posting the solution (the simple graph) below, with a bit of information about how it was garnered. But frankly, if you want to delve deeply into the actual mathematical solution, follow the link to the solution page. You’ll have to scroll about halfway down to get past this weeks riddle, which is a Lord of the Rings based teaser.
Prof Finkel used his riddle solutions program to get an answer, however the truly good information came from a math professor (Raphael Ordonez) who simply worked it out with pen and paper while proctoring his students math finals last week…. Yeah… this guy’s way smarter than any of us….
Here is Ordonez’s run up to the beginning of his solution:
“Upon closer examination, we find that there are five statements dealing with only heroes or fear (Statements 3, 5, 6, 7, 10), five statements dealing with only Tri-D Chess or Fizzbin (Statements 1, 2, 8, 9, 11), and exactly one statement dealing with both (Statement 4). Let’s renumber, and also break up Statement 10:
1A. Troi is feared by the person Geordi fears.
1B. Riker is feared by the person Picard fears
1C. Picard’s hero fears Geordi.
1D. Riker is the hero of Worf’s hero.
1E. Data is the hero of Riker’s hero.
1F. Data’s hero is not Geordi.
2. Worf’s hero ranks 3 times lower at Tri-D Chess than the crew member who is best at Fizzbin.
3A. Picard ranks two positions behind Troi at Fizzbin.
3B. The person who is worst at Fizzbin is better than Troi at Tri-D Chess.
3C. The person ranked number 3 at Tri-D Chess is ranked 4 positions higher than Data at Fizzbin.
3D. Riker is ranked 2 lower at Tri-D Chess than the crew member ranked 2 at Fizzbin.
3E. Geordi ranks 2 at Tri-D Chess.
The puzzle of fears and heroes can be solved on its own, using only Statements 1A – 1F. The fact that each crew member is feared by some other member means that the correspondence issurjective; therefore, it must bebijective as well, and each must be feared by exactly one other member. So we can’t have two members fearing the same member, etc. The same goes for heroes.”
You can see this guy has a superior problem solving intellect. Without further ado, here is the solution to the puzzle, AND the link to the full write-up detailing it! I hope you enjoyed the Star Trek riddle: Six Fearsome Heroes!