This one’s from AMT‘s 2007 upper primary Australian Mathematics Competition. Yes, it’s a while ago, and we are not aware that such BODMAS nonsense has appeared since on the AMC, and of course such BODMAS nonsense is endemic elsewhere. But we hold, or at least held, AMT to a higher standard.

According to the website, students are permitted calculators in the Primary divisions…

So, why even have the question?

(a) FFS. (b) Would that help with this question?

If the person who wrote the question uses the same brand of calculator as the student sitting it… the standard “scientific” calculators have implied parentheses (aka order of operations) pre-programmed.

So to answer (b) I would assume yes for many (n>0) students.

A somewhat ridiculous decision, given that calculators aren’t really useful for these problems at all as far as I can tell.

I learned only today that when calculating a^b^c^d one starts at the top with c^d and works down. I would use brackets but I did not know that there was a widely accepted approach to start at the top. Do others know this?

It was mentioned in https://www.youtube.com/watch?v=BdHFLfv-ThQ

I think the convention is pretty standard, but of course it is sensible and preferable to use brackets.

One is never too old to learn.

It makes sense, if you consider that the brackets are implied. Brackets within brackets, work from the inside to outside.

Definitely not obvious to all and definitely leaves lots of room for error.

My CASIO calculator does it the other way. There’s probably no hard and fast convention. It’s kind of like the implied multiplication thing that everyone was arguing about: does 16/4(2+2) = 1 or 16? My CASIO says something different than google. The only correct answer is that you should always use brackets.

Yep. USBB.

It’s a dumb question for reasons already mentioned, including the fact that students have access to a scientific calculator.

I really don’t see the point in asking questions that deliberately require using the arcane BODMAS crap. In reality, only an idiot would write the expression like AMT has. It seems like simple mathematical common sense of prudently using brackets to remove ambiguity in an expression does not exist. I wonder (in the nicest possible way) whether VCAA would require students to use brackets …?

I wonder what the rationale is for this being a *competition* question.

I don’t think there was any rationale. Even Federer hits an unforced error on occasion.