We rely so much on the web for finding information these days. We even rely on it for providing information we would have remembered in the days before the internet. As a matter of fact, this is probably contributing to the erosion of memory as an innate human talent.
It's also been shown that memory
can be improved if instead of just providing the answer, someone gives us a hint about the answer. We rebuild memories that way in the fabric of our brain.
So, this leads me to the idea. Instead of a search engine that just answers the question outright, let's have a mode where the search engine will return information or hints about the answer instead of the answer directly.
Example:
Who was the lead actor in the movie Jaws?
Instead of just replying with Roy Scheider, the response could be "his initials are RS" or "He was also in Blue Thunder".

Perfect powers in Fibonacci sequencehttp://arxiv.org/pdf/math/0403046v1.pdf Spoiler alert: 0, 1, 144 are the only squares. 8 is mentioned as a cube. [a1, Nov 20 2023]

So now we want our AI to tease us mercilessly until we buckle or run to DuckDuckGo to get the answer that will shut the other, smarter, more maddening search engine OFF? What if we don’t guess correctly? Sit in the corner? Caning? Virtual humiliation by a bot?

While I eagerly await developments in AI, I don’t need some smart-ass 20-questions moderator to tease me until I remember the date of the Norman Invasion. Having retained this knowledge forever due to the ponderous Socratic method employed on me that gave me a headache, I will probably never need it again. But it is now taking up room it does not deserve. We should get to choose the priorities of what we store.

Anyway, this idea could be extended to all online systems.

Maps app...
Directions
From: current location
To: 27 Acacia Avenue, Bridge Crossing, Lowertown
Proceed to the end of the street and turn in the correct direction.
Continue for a certain distance, turning where appropriate.
At the landmark, turn left, but not the landmark you first think of.
Hold your finger in the air if you feel lost.

Online Banking App:
Enter your secret code to log in
* * * * * * *
Your balance is slightly less than you thought it was, but not so low as would cause you major problems.

Email client
New Messages: there are a few.
Message 1. From: someone you know. Subject: about someone else you probably know, but might not. Message body: There was an event that a certain person didn't go to. See if you can guess whether you did the right thing or not. It seems quite urgent to your correspondent. [Reply] [delete] [forward to a random entry in your address book]

********
Would you like a hint? Your first pet.
********
Sorry, that’s not correct. Would you like another hint? Who was gored in the 1888 Pamplona run?
********
20 minutes later…

Sorry, that’s not correct. How long do you want to do this, you moron?
For $20 we’ll send a temporary password. For $50 you get to change it to something you can remember, doofus.

[pocmloc] I would actually like push notifications from my bank that told me things like "The integer part of your current balance is both a square and a Fibonacci number!"

Yeah, I got something similar on a couple calculators I tried, seem to fumble on big numbers. Work it out with a pencil? Nah, I just googled big number calculator and tried a few more.

1244190 * 1244190 = 1,548,008,756,100

Edit to add - I just noticed you don't even need to do the calculation to see the first answer was wrong. If X ends with a single zero, then X*X has to end with TWO zeroes, right?

Heh - Bing can learn from its mistakes. I asked again a little later...

ME: What is the square root of 1548008755920?

BNIG: The square root of 1548008755920 is approximately 1,244,190.

ME: Can you be more previse? I'd like a reply accurate to 4 decimal places

BING: The square root of 1548008755920 is approximately 1,244,190.0000 to 4 decimal places.

ME: How much is 1,244,190 X 1,244,190?

BING: The product of 1,244,190 and 1,244,190 is 1,548,008,756,100.

ME: If "The product of 1,244,190 and 1,244,190 is 1,548,008,756,100" how can "The square root of 1548008755920" be 1,244,190?

BING: I apologize for the confusion. You’re correct. The square root of 1,548,008,756,100 is indeed 1,244,190. However, the square root of 1,548,008,755,920, which was the original number you asked about, is approximately 1,244,189.9999 when rounded to four decimal places. I appreciate your patience and understanding. Let me know if there’s anything else I can assist you with.