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Category Archives: puzzles

Because you’re the one talking about other people’s state of mind.

That’s how I know your state of mind is scattered: because you’re looking into your own mind for your conclusions … and finding someone else’s. There isn’t actually a way to observe emotions. You really aren’t Yoda.

Here’s the thing: if you’re wrong when you ‘conclude’ based on your desire to be right that someone else is mad or sad or whatever, who will detect your mistake first?  They are actually an authority upon themselves, and you probably aren’t a psychologist with a brain-wave reading device.


So how do I know it’s you projecting?

Because it’s you talking about emotions while having zero evidence and lots of motivation to make things up.

Of course the best part about this spell-form is that once you’ve projected, everyone knows about yours. If you get stuck lying to yourself about what’s happening, you’re the one sharing with the group full-time.

This is actually a really hard problem – it’s a really neat problem for students of calculus, but it’s hard, like 4 or 5 stars hard. This puzzle is also a real problem, meaning it actually saves someone some hassle or energy or time or money. As with many word problems, if you imagine yourself in the situation, or on the hook for the outcome, you might find it easier.

It was first encountered by Welches, the grape jelly manufacturer, while making their primary product, grape jelly.

Standard jelly- or jam-making means cooking fruit juice to drive off the water and make it more concentrated. But heating is expensive, so naturally people sought low-temperature ways, and the easy way is evaporation by moving more air, and exposing a larger surface to the air.

One easy way to get more jelly to dry out is to spin a wheel in it, so that the jelly is lifted out of the pan on the wheel, increasing the surface area exposed to the air.grape_wheel

If you only barely dip the edge in, only the circumference of the wheel gets wet, and only the edge really works to increase the surface area of the jelly exposed to air, although it is almost the entire edge – all but the tiny bit dipped, which is protected by the liquid.

If you dip the wheel half way, so that the axle itself is in the liquid, too, then half the wheel is under the surface of the liquid, which doesn’t expose anything to air, although then you do get the entire top half of the wheel wet, which means at least half is exposed to air.

Of course one obvious way to increase the wet exposed surface is to have lots of wheels, which of course they all do, now. But it’s still worthwhile to make each wheel maximally efficient.

If we set the wheel at exactly the right height, then we can maximize the amount of surface of the exposed, wet wheel.

So what is the proper distance of the axle above the surface of the liquid, to maximize the wet, exposed surface?

The standard way to answer is in terms of a fraction of a radius as the picture suggests.


Then mistakes wouldn’t exist.

What, you never make mistakes?

Super: God himself dropped by my website.

…and got lost.

I never believed those crazy UFO nuts ‘till just a couple weeks ago. I never thought something like this could be real.

It all started one late night as I was headed home after visiting some friends that lived across town. I apparently took a wrong turn, and soon didn’t know any of the landmarks around me. I was looking for a familiar area so I could find my way back, when suddenly this bright light snapped on and blinded me momentarily.isle

They must have come over to me while I was dazed, because next thing I knew they were carrying me onto this shiny vehicle with strange, flashing lights on it. I couldn’t understand them at all, and I don’t think they could understand me, even though they seemed to have a translating device. It would talk in their language at random times, and both of them would stop and listen, then look at me.

Their bodies were a lot larger than ours, and I think they breathed a different atmosphere than we do, because before they actually put me in their ship, they stuck this smelly tube in my face. But I think now it was so I could breathe in their atmosphere because there was this little machine with lots of lights on it attached to the tube. I figure it put some little doo-dad in my lungs or something.

They also had some kind of force field that separated us, probably to protect us from each others germs, but I could still smell them.

brainscannerThen we took off. After a short and bumpy ride, we evidently arrived at the mother ship, because there were a bunch of these pointy-headed aliens all over. I think they must have drugged me and done some kind of examination on me, cause I remember being stuck in the arm with a needle, and now I’m kind of sore in some bad places to be sore. And I think I had a seizure or something because my elbows and knees were all dinged up, and my face hurt a lot.

I’ve thought a lot about it, and I think I figured it out. The aliens test new drugs on people then just dump them somewhere for the cops to find, naked and confused, cause I woke up the next day in jail with bandages on me. The judge stiffed me, too. So not only did I get all bunged up with some stupid aliens, but I had to pay a $50 drunk and disorderly charge, and now they got me in some program where I don’t get to go outside by myself.

Aliens are such assholes.

The Bear Hunter

This is a mapping puzzle. Drawing a picture, or having a map hugesatmight help. Part one is 3–out-5 difficult (unless you’ve heard it). Part two is 5-for-5 hard.

 Famous part 1

 A man leaves home, and walks a mile south.

 He hasn’t found a bear, so he turns east, and continues walking.

After a mile of walking east, and still seeing no bears, he turns north.

 After another mile of walking, he arrives back home, where he finds a bear rooting through his garbage, so he shoots it right there on the spot (with a camera!)

 What color is the bear?

If you are finding that something doesn’t quite add up, consider that one of your assumptions might be false. molly

Seek a new angle by which to consider the situation, or by which you might discover which assumptions you’ve made without noticing. What could you change, that would make things add up correctly?

Challenge part 2

The correct answer is not obvious to everyone at first glance, because it seems like something is amiss, but it all makes sense upon consideration of the situation.

Well it was recently discovered that such a situation can occur somewhere else entirely!

In fact, there are an infinite number of places…where are they, exactly?


I really like this puzzle because it does such a good job of illustrating the essential approach to all problem-solving; identifying principles working together, then using them to narrow down the possibilities, ideally to just one result.

Sherlock Holmes’ most famous line teaches the same lesson: “once you have eliminated the impossible, whatever remains, however unlikely, must be the truth.”  (His line, “Elementary, My Dear Watson” came from an American movie – it appears nowhere in A. C. Doyle’s books about Sherlock Holmes.)

We can begin such puzzles by taking an inventory of principles, which means writing down or thinking of everything we know that must be true in our situation. We really have little else to work with in an open-ended situation, and indeed, the entire history of science can be considered the (re)discovery and use of such relationships.

It may have been a while, but for this puzzle, if you write down everything which is true for all circles and all rectangles, you’ll be able to identify the two which work together to force X to be a particular size, and not some other. You’ll know when you’ve found the right ones, because you’ll immediately know what the answer MUST be, based on the logic and that is the entire point of working that way; so that you can make your own judgement about it, and can trust it, and will know that you can trust it.