It’s Friday afternoon and fourth period is almost over.
“Okay, just a reminder — there will be a surprise quiz sometime next week on the last three chapters!” the teacher brays as the bell rings and the students begin to shuffle out.
In the hallway, Alice looks to Bob and says, “Dude, what a crock. Mrs. Trunchbull sucks. I hate surprise quizzes!”
“Me too! You can waste the whole week studying. I’d rather just cram, take the text, and expunge.”
But then a thought occurs to Alice. “Wait a minute — she said there’s going to be a surprise quiz sometime next week, right?”
“Right…” Bob slams his locker shut, and they walk down the hall towards their fifth period class.
“But we know the test can’t be next Friday, or else there won’t be a surprise!” Alice exclaims.
“What do you mean?” Bob asks.
“Well, say she’s secretly planning on giving the test on Friday. But we know that the test is sometime next week only. So by Thursday afternoon, when she hasn’t given the test yet, we’ll know that the test has to be on Friday — no surprise!”
“Dang, I see.” Bob’s eyes open wider. “Hold on — it’s crazier than that. It can’t be Friday, right? But then it also can’t be Thursday either! Since when Wednesday afternoon rolls around, and she hasn’t given the test yet, we’ll know it can’t be Friday — as you just explained — so it must be Thursday. But if we know it has to be Thursday, that would eliminate the surprise too!”
“Wow, this is awesome. And by the same logic, it can’t be Wednesday either…”
“… or Tuesday …”
“… or Monday!”
“Holy smokes… it seems like she can’t possibly surprise us,” Bob says with a grin.
Alice frowns. “And yet I still have no idea when the quiz actually will be.” The bell rings for the start of fifth period, and the pair make their way into the classroom. “We’ll have to figure out what this means after class.”