Six at the Circuit

Question

There were six friends: Charles, Claude, Lee, Konrad, Peirce, and Shannon. For the most part, all were truth-tellers. However, Konrad tended to falsify claims more often than not.

All decided to meet at the circuit to bet on the local racers. Peirce and Konrad met Shannon at the gate. Neither Charles nor Lee arrived with Claude. So the four waited.

While waiting, Konrad came up with an idea. He suggested "Since, I know more about these racers - even more than Shannon or Lee combined - I thought it would be fair to split us into betting teams. You'd still bet by yourself, but you and your teammate split the winnings."

Claude and Shannon agreed with Konrad, with Shannon adding "betting should be secret so teams can't work together." Peirce, however, didn't say anything as all they could think was "Please not Charles. Please not Charles. Please not Charles."

Finally, Charles and Lee arrived shaking Peirce's hand first, and moving on to the rest. Konrad explained the plan and received no resistance from Charles nor Lee. All that remained was choosing teams.

Peirce, mostly because they wanted to avoid being paired with Charlie, blurted out "Seeing how I know as little about these racers as Charles and Claude, why not allow us to pick from you 'experts'?"

Peirce snatched Lee's hat right off their head and produced a small notepad, saying "We'll put Lee and Konrad and Shannon's names into Lee's hat. Charles and Claude can pick before me."

After a quick bout of "Rock, Paper, Scissors", Charles was determined the winner. Reaching into Lee's hat, Charles drew not Shannon or Lee, but Konrad! Charles was especially excited as he was known to be not so knowledgeable of racing, while Konrad excelled.

Claude placed his hand in the hat next, drawing Shannon's name, and passed the hat to Peirce, who simply dumped the hat back onto Lee's head. Lee shook out the remaining piece of paper, and the group headed into the stands.

The group began secretly placing their bets. Peirce started overhearing Konrad or Charles whispering something about car #5, but Shannon soon intervened, scolding them with "This is the first round and you're already cheating? I would expect this from Konrad, but not Charles."

Dejected, Charles moved one spot away from Konrad and the group continued placing their bets. Once everyone was done, not Peirce, but Lee offered his own hat to store the paper. Everyone tossed in $5 along with their predictions. After several minutes, the race flags began waving and the racers were off!

The group sat in anticipation as the cars zoomed around the course. Charles could be seen sitting on the edge of his seat, seemingly cheering for car #5. The final lap was coming up and it was clear either #5 or #9 would win.

As soon as Lee noticed #9 was in contention, he jumped out of his seat and began whooping. Charles too leapt from his seat, and made it obvious he was backing #5. Feeling left out, Peirce and Shannon stood up, followed by Claude. Konrad remained seated.

The cars flew around the last bend to the final straightaway - their noses even. It was going to be a photo finish. Both cars passed the finish line, but from where they were sitting, the group couldn't clearly tell who had one. Finally, over the loudspeaker, the announcer said "Well folks, I hope you enjoyed that race. It was certainly a close one, but in the end the winner was….car #5!"

Charles began jumping for joy as Lee slunked back into his seat. Neither Shannon nor Claude congratulated Charles. Konrad merely sat with a smug look of pride. Peirce piped up "Why are you so happy, Charles? It's obvious Konrad picked #5, and you just happened to be on his team."

Without saying a word, Charles grabbed Lee's hat and began reading off the bets. "Let's see here...Peirce picked #3 (which was last by the way)" The group laughed. "Shannon and Claude both picked #1. Lee chose #9, obviously. So Peirce, that leaves myself and Konrad."

Charles lobbed the hat into Peirce's lap. Peirce gazed into the hat and a look of bewilderment slowly took over their face. The person who bet on #5 was not Konrad, but Charles. Konrad high-fived Charles saying "Atta boy! I knew I'd rub off on ya."

Konrad grabbed the cash and began splitting it up. He paused, handing it all to Charles saying “here, you deserved this.” Konrad’s actions were not expected by Shannon or Lee or Claude or Charles.

Peirce, preoccupied with guilt, stood up and placed a hand on Charles’s shoulder. “Ya. You earned it.”

What is everyone's state of mind following these events?

--

A hint of sorts:

the answer is not so important, and could be interpreted differently. I'm more interested in how the conclusion is made.

Canadian Thanksgiving hint:

what happens in the story is irrelevant.

Answer 1

The names of four of the six gamblers must be a reference to

Charles Peirce and Claude Shannon, two early contributors to the theory of logic circuits - hence why the racetrack is called the Circuit.

I'm not sure if the last two names were meant to refer to anything -

I couldn't find any relevant Konrad Lee or Lee Konrad, but possibly Lee de Forest and Konrad Zuse? (I found these names simply by searching the Wikipedia page on logic gates for the words "Konrad" and "Lee".)

My theory is that the six bets made by the gamblers were

some logical combinations - probably AND, OR, NAND, NOR, XOR, XNOR in some order - of two basic possibilities, perhaps car #5 and car #9 since these were the last two in the running towards the end of the race (although the mention of car #3 for Peirce and #1 for Shannon and Claude does admittedly go against this hypothesis).

Some more word choices within the story may be intentional hints:

• Konrad mentions knowing more than Shannon and Lee combined.

  Maybe this signals something to do with an AND gate?

• Peirce repeats the words "Please not Charles."

  Maybe this signals something to do with a NOT gate?

• There are, of course, many instances of the words

  "and", "or", and "not" throughout the story. I'm not sure how many, if any, of these are meant to be clues.

• The final question about everyone's "state of mind" probably means

  that we have to deduce the True/False state of each one of the six statements associated to their bets.

The pairing (Charles and Konrad, Claude and Shannon, Peirce and Lee) must be significant somehow, but I'm not yet sure how this works out. Given the "Please not Charles", I'll guess that

Peirce's bet is the exact opposite (NOT) of Charles's.

And given the first bullet point above, perhaps

Konrad's bet is the AND of Shannon's and Lee's? But that would mean he only wins if they both do. Perhaps the OR would be a better bet (pun intended), although again that would make the team formation a bit weird.

This is only a partial answer so far, but I'm quite sure that I'm onto something.

Answer 2

Building on rand al'thor's answer, still a work in progress

I think the gates are AND, OR, NOT, NAND, NOR, XOR (Exclusive OR sometimes EOR). Now Lee gets his hat taken off and that makes me think of the NOT symbol which is a little flat hat. Furthermore I believe that Pierce is the NOT symbol as he is constantly removing and adding the hat to Lee. Possibly L, K & S are all NOT NAND and NOR since they are all put into the hat.

Then

Possibly the pairs are all their associated opposites. I believe Pierce and Lee are NOT and XOR since they were paired up 'by default' after the others picked. As for "Konrad falsifies claims more often then not" makes me think he is the NOR or AND functions which returns a false value in 3/4 of cases. I'm leaning toward NOR since he's in the hat. However it is difficult to align this with the fact that K > L U S. If the above assumptions are correct then Lee is XOR which is only false if A&B are both True. Therefore something is wrong in my assumptions....

And

The standing up could be gate activation in a logic gate, but I'm not actually familiar with them. More statistical logic statements. I'm going to keep working on this, but I think I might be reading into some of this wrong. I'll let it sit for a bit and come back.