It was just a matter of time

So it's a long weekend in the US and Canada this weekend, and as such it's easy to let your mind go a bit soft while you're away from work. I know nothing of this, of course, as I'm still unemployed. All the same, I thought I might present you, my dear readers, with a little puzzle to think over to keep your mind fresh and active.

One of the upsides about doing job interviews is occasionally being presented with a very interesting logic puzzle. Of course, most of the puzzles are really rather mundane, and even the best ones tend to be quite contrived, so I thought I might pose a puzzle to you that is in fact drawn from my daily life.

You see, I have a digital clock in my kitchen that doesn't always tell the right time. Usually it's quite accurate, but often it's mysteriously a few minutes off. If you were to observe this clock for some time, you might notice that the rightmost digit for the minutes counts quite oddly. The sequence is: 0, 1, 2, 3, 4, 9, 8, 7, 8, 9, and then back around to 0 again to do it all over.

The cause of this bizarre acalculial malfunction is deceptively simple. Can you figure out what it is?

Jet Airliners, Tractor Pulls, and Math

Recently a friend of mine made a post about the AF-447 crash and some of the human factors involved. One of the things he noted was that the thrust levers were not designed to indicate, by their position, the current thrust setting of the engines they controlled. At first glance, this seems an odd decision, but there is indeed a method to the madness.

Before we dive into that method, we first need to take a little detour through the deliciously redneck world of competitive tractor pulling. Yes, you read that right, tractor pulling...

So, what is it you *do* here?

Sometimes people ask me what it is I do. This is the answer, roughly speaking. (scroll down, for some reason the second video is at the top, but they're in the correct order below that)

Two more marks

I (unofficially) scored an A+ in Advanced Calculus, and an A in Applied Algebra. Add this to the A in Rings and Fields, and the only unknowns are Nonparametric Stats and Number Theory.

I am pleased.

Two down

The exam Rings and Fields went very well this afternoon. I only missed one question which was 2 marks out of 100, so I think I should come through with quite a nice mark.

One down

Got my Advanced Calculus test out of the way yesterday afternoon, and I'm quite happy to say that I did quite well with it. I did muck up one or two questions a bit, but in the end I think I should be good for 90% or so.

Now I just need to get through Rings and Fields, Non-Parametric Stats, Applied Algebra and Number Theory.

Page Mill Road, Part 2

So today I decided to give Page Mill Road another run. I took a slightly different route (went up Altamont Rd instead of Moody Rd) but it ended up being about the same.

I did it in the same time as last week, 1:45 going up and 0:30 coming down, though I had fewer near-death experiences on this descent.

I figured rather than paste in the same map as the previous blog post I'd do some interesting calculations instead.

Assuming a 210lb combined weight for me and my bicycle and 2200 vertical feet of climbing and ignoring wind resistance (I really wish I could ignore wind resistance), I would have to have output a minimum of 150 kilocalories to reach the top, and I would have output this energy at an average of 100 watts; if I could get that up to 250 watts I could get to the top in just over 40 minutes and go ride the Tour de France. More realistically, if I dropped about 25lb of weight I could cut the time down to 1:30 with the same power output.

On the way back down, all that energy was returned to me at an average of 350 watts, or roughly ½ horsepower.

And now you know.

Fun with math

First off, let's get this video link out of the way.

Now that I've scared you all off, I'll get to the meat of this blog post, which is the oft-ignored 5-function pocket calculator.

I'm sure you're all familiar with what a 5-function calculator is. It's those really simple calculators that do addition, subtraction, multiplication, division, square root and percentage (and if you're paying attention, you'll notice that's 6 functions).

Everyone is pretty familiar with the basic functions. You press "1 + 2 =" and get 3, you press "5 x 6 =" and get 30, etc.

But what about the square root and percent keys? Or those "M+, M-, MRC" keys? Most people might never think to press those buttons, so let's take a look at what they do.

First up is perhaps the simplest key on the entire calculator: the square root key (that's the one that looks like a checkmark). It takes one number as its input, and spits out its square root. Let's try to apply that...

Let's say I want to mount a webcam in the top corner of my wall, but my computer is all the way down on the floor at the other end of the wall, we can use the pythagorean theorem to find out what length USB cable I need.

Since my wall is 12 feet wide and 8 feet tall, we punch in "12 x 12 =" and write down  "144", then type in "8 x 8 =" and write down "64", then we enter "144 + 64 =" and hit the square root key to get 14.4 and change, and resolve never to touch a calculator again because that was a royal pain in the ass to punch in.

But we can do better, if we use the calculator's built-in memory. First, we make sure that the memory is clear by examining the display for a little "M" icon that would indicate a stored value, and we begin. This time, we type in "12 x 12 M+" and the display indicates "144 M" showing us that it has remembered this value. Next we type in "8 x 8 M+", and the display shows "64 M". Next we hit the "MRC" button and magically the calulator shows us "208", which is the sum of 144 and 64. We hit the square root key and get the answer 14.4 and change again! Hooray!

But wait, we can still do better. On most 5-function calculators, the multiplication key has a hidden function: if we press the keys "12 x =" we see that the display indicates 144 without having to enter in the second 12! So now all we have to type is "12 x M+ 8 x M+ MRC" and hit the square root button and magically the result 14.4 is there plain as day!

Moving on, let's say you're out for dinner and you want to calculate what size tip to leave. The cheque comes out to $23.81 and you want to leave a 15% tip. How much money do you leave? Well just whip out your trusty calculator and press "23 . 81 + 15 %" and we can see that we should pay a total of $27.38.

Alternately, let's say you're shopping for a new TV, and you know that your friend can get you an 11% employee discount. You look at a model costing $1199 and you whip out your trusty calculator again, punching in "1199 - 11 %" and get $1067.11. But wait, what about the 13% combined sales tax? punch in "+ 13 %" and we see that the grand total is $1205.83, without the extended warranty. How much did that 11% save us? Punch in "1199 x 11 % + 13 %" and we get $149.04 (alternately, you could punch in "1199 + 13 % x 11 %" and get the same answer).

But let's not stop there, how about reciprocals? Like, what's 1/16th in decimal? As a percentage? Punch in "16 ÷ =" and you get 0.0625, punch in "16 ÷ %" and you get 6.25%. What percentage is 19/32nds? Punch in "19 ÷ 32 %" and we get 59.375%.

It's really worth spending a little time to get familiar with your calculator. You'll find that only having "5 functions" isn't very limiting at all, and you never know when knowing a few calculator tricks might come in handy.