## The Potato Puzzle

###### By Anupum Pant

Some call it the Potato paradox, but I prefer calling it a puzzle. It isn’t really a paradox. It’s just that we tend to get confused easily when working with such problems and most times end up with the wrong answer. Here’s the question:

You have 100 kg of potatoes. Assume that they are made up of 99% water. Now, you keep them outside to dry for a while. When measured for water content now, they contain 98% water. What do you think is the weight of these dried potatoes now?

Answer quickly first. Then, try and calculate. It isn’t really tough.

Take 15 minutes, or more if you have to. Use papers, pens and calculators if you have to. But whatever you do, stay honest. Don’t search for the solution on the internet, or don’t read further if you haven’t done it yet. Trust me, your brain won’t like the answer.

Solution – [Wikipedia]

For the explanation, watch this visual explanation…

## A Thread Around the Earth

### Background

Couple of days back, I read about a puzzling geometrical conundrum, probably on Quora. It might not sound amusing to you math geeks out there, but to me, it sounded like an impossible thing at first. The sad part is, I did not save the source link in my notes. Thankfully, I did care to note down the idea. Let me call it the “Thread wound Around the Earth” puzzle.

Here is a simple question first. Try answering it without any calculation. Just guess. Be honest to yourself, don’t see the answer just below it. Scroll slow.

As BBC’s website puts it…

Imagine a piece of string wrapped around the Earth’s equator – that’s about 40,000km. How much MORE string would you need for it to sit 15cm above the ground, all the way around?

A) 1 metre, B) 1 kilometre or C) 1,000 kilometres

### Thread wound around the Earth

The answer is A) 1 meter. Yes, just 1 meter of extra rope.

Suppose, you have an outrageously long thread with you. You tie it around the base of a tree, somewhere at the equator. Now, you go around the earth, along the equator, carrying the thread with you, till you come back to that tree where you started. At this point, you’ll have a thread that goes around the earth in a circle. At every point, let us imagine that the rope is taut and touching the ground (there are no mountains or valleys in between). It’s a perfect circle (assume).

Suppose, you still have an extra meter of the rope left now. So, you break the wound rope at one point and add the extra meter to it. That of course slackens the wound rope. For this rope to be taut again, it has to be lifted up by some amount. What do you think that distance would be from the ground? Assume that the rope still makes a huge circle just above the ground and lifts by equal amount at every point along the equator.

Just the extra meter of rope, causes the rope to rise by ~15 cm all around the earth (actually 15.9 cm). For a single meter of rope added to a 40,000 km of rope, that sure seems like a huge lift! But that isn’t all…

The most amazing part is that, no matter what the size of the circle, a meter of increased circumference will increase the radius by ~15 cm. Always!

Try tying a rope around a golf ball, or even try doing that around the sun. It’s always that – 1 meter increase in circumference, always increases the radius by ~15 cm.

### The Math is so straightforward.

If you think about it mathematically, it is completely straightforward.

Radius X 2 X Pi = Circumference

That means, the Radius is directly proportional to the circumference of a circle. Everyone knows that. So, the amount of change in the radius is reflected proportionally in the circumference, the magnitude of radius can be anything, really. So it’s pretty natural that just a single meter of rope is required to lift the rope by 15.9 cm around any circle. The size doesn’t matter. But practically thinking, the above question makes it seem impossible.

Please hit like if you learnt something from the article.

## Ultimate Problem Solving by a Crow

### Background

I know I wrote about how smart crows can be a few days back, but even when I wasn’t particularly searching for amazing crow videos, I happened to stumble upon an astounding video of a crow solving some puzzle. I was so blown away by this, that I couldn’t resist sharing another crow post in under two weeks. Hold your hats because this crow, nicknamed 007 will blow them off your heads.

Side note: Want to see a chimpanzee blow your mind? Watch him do a task that more than 95% of the humans wouldn’t be able to do as well as he can do it. – [Working Memory – Chimpanzees vs. Humans]

Alex studies wild birds which he releases after 3 months of research. This one is nicknamed 007 and it is about to attempt what Alex believes is one of the most complex tests for the animal mind ever constructed. The bird is familiar with the individual objects, but this is the first time he is seeing them arranged like this.

This video comes from a BBC show called ‘Inside the Animal Mind‘ hosted by Chris Packham. [Video]

In the video, a wild crow, previously not having learnt anything about the 8-part arrangement of the puzzle, manages to solve it with ease. I would have taken some time to figure out the solution.

8-Part sequence

1. The crow pulls out a small piece of stick from a thread.
2. It then approaches a box containing a piece of food and figures that it would need a longer stick to get it. It moves on with the smaller stick to take a stone out of another box.
3. Takes out another stone
4. And one more
5. Drops one of the three stones in a box which needs the weight of all three to release a longer stick.
6. Drops the second.
7. And the third. The longer stick is released. It takes the long stick.
8. Finally, the crow uses the longer stick to pull out food from the box mentioned in second point.

### How I try to believe it

Although when I say that the crow wasn’t aware of the arrangement, I mean to say that it wasn’t aware of the sequence in which the puzzle was meant to be solved. It seems as if it was trained with the individual tasks.

I’m guessing that the crow was trained for some time to complete the individual tasks separately and not in a particular sequence. The 8-part sequence was probably shown to it for the first time. I may be wrong. But, I think when the speaker says, “The bird is familiar with the individual objects“, my interpretation makes sense.

If I’m wrong, I yield and state that crows are just too intelligent and are going to take over the world in a few hundred years.