Very Clever But...

There's an article saying the largest number you can represent with three digits is 9^9^9 which tallies up to:

196,627,050,475,553,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

or

1.96627050475553x10^77

Which is very clever, except...

The asshole is making an assumption, just like the teacher he's castigating.

The teacher's defense of the answer being 999 was that exponents had not yet been taught.

OK, Mr Clever.

Will your defense be that we haven't covered alternate bases?

Because in hexadecimal the largest number is f^f^f.

That's 4.17381588438865x10^264.  That's a lot bigger, isn't it?

In Octal the largest is 7^7^7.

That's  2.56923577521059x10^41.  That's a lot smaller, isn't it?

So really the largest number we can express in three digits is undefinable unless we either make assumptions or give definitions.

Hurray!  Everyone gets to be right, and wrong.

Guess what else you accomplished by forcing the answer to be 9^9^9 for all of those students who had not learned exponents and answered 999.  You've taught them it doesn't matter if they bother to learn because someone can come along later and edit their scores.

You're haven't taught them to question authority, they aren't old enough to understand what that means.  You've taught them that some asshole parent can come along later and fuck them.  You've taught them that doing well doesn't matter because you couldn't take that your special snowflake daughter wasn't paying attention to the lesson being taught and, like you, gave a too clever answer.

Part of learning is to determine the answer being called for, not just an answer that fits the criteria.  Your daughter had better enjoy being a spinster professor of math, because you've put her on the track to be VERY VERY alone and isolated.