christianp, 21 days ago

@ColinTheMathmo got my pen and paper out, jotted off number 1 easily, then looked at number 2 and thought, "you know what, I don't need to do this"

RobertJackson58585858, 21 days ago

@christianp @ColinTheMathmo

Use induction. Yes. Use induction with the answers at the back of the text book

Q1 is the straightforward base case.

The back of the text book has the answer to Q k and Q (k+1).

QED.

faelif, 21 days ago

@RobertJackson58585858 @christianp @ColinTheMathmo

Not so! It may have Q20, but not Q21

RobertJackson58585858, 21 days ago

@faelif @christianp @ColinTheMathmo

clutches at straws

Mod20?

ColinTheMathmo, 21 days ago

@christianp Yup ... exactly so.

gjm, 21 days ago

@christianp @ColinTheMathmo Eh, I thought they were kinda fun. In every case it was an exercise in "can you spot the trick?" and enough of the tricks were at least semi-interesting to hold my interest.

(Except maybe for 16, which feels like it should be straightforward but somehow isn't working out for me so far. I suspect I've done something stupid or missed something easy, and it does fall under the rubric of "spot the trick that makes it simple" even though I either haven't spotted it or have screwed it up.)

I'm old and slow (at least compared with when I was younger and quicker) so I certainly didn't do them all in 20 minutes.

The "finals" problems at https://math.mit.edu/~yyao1/pdf/2024_finals.pdf are ... somewhat tougher.