Arbitrage between puts struck at 80 and 90

On the same stock and with the same expiry, a European put with strike $80$ sells for $8 and a European put with strike $90$ sells for $9. Can you make an arbitrage profit?

Yes. Buy $8$ puts at $90$ and sell $9$ puts at $80$: the cost is $72-72=0$. At expiry the payoff is $0$ if $S_T\ge90$, $8(90-S_T)>0$ for $80\le S_T<90$, and $S_T>0$ below $80$, so you never lose and gain whenever the stock ends below $90$. The underlying rule: put prices are convex in strike with $P(0)=0$, so $P(80)$ must be strictly below $\tfrac{80}{90}P(90)=8$ when the stock can finish below $90$.