Oh dear. I’m afraid my attention wandered when compiling this month’s diary. I gave the solution to the August brainteaser as 64. A more subtle approach shows that 32 is in fact the lower bound. I am obliged to Michael Tarski for this. The embarrassing thing is, Michael sent me his solution earlier in the month, I read it, though “That’s neat!,” then forgot it. Too much going on here. Apologies to Michael, whose solution is here.