Obsidian Wings

Something Completely Different

by Michael Cain
(submitted by request)

A recent comment thread headed off into a discussion of the attractions of games and puzzles that involve combinatorial search, like Wordle or Sudoku or Freecell. Here's an example of a combinatorial puzzle. My daughter brought this home from math class when she was in eighth grade (long ago).

On the way home from work I stopped at the corner convenience store to pick up four items. The checkout clerk did things on the register and told me "$7.11, please."
"That seems too much. How did you calculate that?" I asked.
"I multiplied the four prices together."
"Aren't you supposed to add the prices?"
"Oh, right." After a moment he said, "Still $7.11."

What were the prices of the four items?

She told me the math teacher was explaining a technique he called guess and check: guess at the answer and check to see if it's correct. She thought it was stupid and clearly expected me to think the same. She was surprised when I said, "Cool! There's a whole bunch of neat math in there!" We talked about problems where you had to choose from a set of possibilities and had to find the right combination to solve the problem. That you often needed to find a clever strategy so you could find the right combination in a reasonable amount of time. We played around with this particular problem some, but didn't guess the right answer before it got tiresome. (No one else in the class guessed the right answer either.)

Some years after that I was working at an applied research lab that did lunch-time technical talks. I was asked to do one that had some math, some entertainment value, and that most of the staff would be able to follow. My recollection of the talk about the 7-11 problem is reproduced below the fold.

Oh, and open thread, because why not?

Negotiating in Good Faith

by wj

An Open Thread for the New Year

Today, for the first time since 1923 (that's right, a whole century) the US House of Representatives failed to elect a new Speaker on the first ballot. (Or the second or the third.) McCarthy could afford to lose no more than 4 votes. He lost 19 -- and 20 by the third ballot.

Not surprisingly, the Democrats were kicking back and enjoying the show. The iconic image was Representative Ted Lieu posing with a bag of popcorn.

I was amused by the exasperated comments of several of the Republicans who are not part of the holdouts. The recurring theme: McCarthy's opponents are "not negotiating in good faith."

Well duh! First, they don't believe in good faith. Second, they don't believe in negotiation. And third, the only thing the House needs a Speaker for is if they want to , you know, govern. Or even just hold hearings/witch hunts, etc. These guys mainly want attention, and they are getting that. Who knows how long it will take them to get tired of the game. (McCarthy's strongest ally is their short attention spans.)

I've seen a variety of speculations about who the Republicans might settle on, if McCarthy continues to fail. Just to add to the mix, I could see a handful of the less conservative Republicans, those who actually have an interest in the quaint concept of doing the job, deciding that the easiest way to the necessary majority is to bite the bullet and vote for . . . Minority Leader Hakeem Jeffries. Sure, they would be vilified for it. But at least something would start moving. Granted, it's a wildly improbable outcome. Then again, has anybody got a more likely one?