Diagram courtesy of puzzle winner, Blaine
I’ll always remember Portland, Oregon, as a place of hyper-kinetic activity — a place where the surprising number of people walking around downtown with canoe paddles did so like jolly dwarves from a Disney movie and the geese sharing space with hippies on the common lawns honked a couple notes higher. Or maybe it was the coffee.
Yes, come to think of it, I might’ve had four days of too much coffee. But thanks to your help, I avoided complete caffeine paralysis (if barely). For those of you who missed it, here was last week’s coffee conundrum:
Each cup gives me a jolt and then the jolt decays across time according to the following equation (t in minutes): Jitters=10-[(t-10)^2]/10
So at minute 10 after consuming a cup of coffee (which, for the purposes of this puzzle happens instantly), I reach a maximum of “10″ jitters. At a combined 20 jitters, I go catatonic. With what frequency can I instantly consume coffee without the combined jitters passing this important tipping point?
Many of you made good use of technology ranging from Perl to Excel to Matlab. Here’s code for the last, submitted by Tim:
%Single Cup Profile
t = 0:.01:20;
onecup = 10-(t-10).^2/10;
cupduration = 20;
timeend = 80; %in minutes
time = 0:.01:timeend;
jitterlimit = 20;
for i = 1:.01:20; %test 1 to 20 minutes intervals
cupnumber = floor(timeend/i);
totaljitters = zeros(1,(timeend+20)*100+1);
for j = 0:cupnumber
currentcuptime = (j*i)*100+1:(j*i)*100+2000+1;
currentcup = zeros(1,(timeend+20)*100+1);
currentcuptime = int16(currentcuptime);
currentcup(currentcuptime) = onecup;
totaljitters = totaljitters + currentcup;
end
if max(totaljitters) <20
max = i;
break
end
And done the old fashioned way, you can see that jitters hits 20 at 5*2^(1/2) minutes, or just over 7 minutes. I can (and did…) drink a cup of coffee every seven minutes without going catatonic. Congrats to this week’s winner, randomly chosen from the pool of correct entrants, Blaine! The rest of us can use the code GEEKDAD59MJ to get $10 off a $50 order at ThinkGeek.
Congrats and thanks for playing the puzzle! And don’t forget to come back Monday, when Judd will drop another installment of PotW.
