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Can You Solve This River Crossing Puzzle?

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River crossing puzzles are a classic form of logic puzzle. In them, you're provided with a scenario—some number of entities trying to cross a river using a raft or boat—and a set of constraints (typically, some of the entities might eat each other under certain circumstances).

In the TED-Ed video below, we tackle a variant of the puzzle in which a group totaling six, three lions and three wildebeest, need to cross a river using a raft. Only two animals can go at once. The problem is, if the lions ever outnumber the wildebeest, they'll eat them. How can they all cross the river?

The larger question of this puzzle is how should we solve such puzzles? In the video, the narrator walks through this solution, but explains how it can be generalized by drawing up decision trees. At each step of the puzzle, you lay out all the possible options, then cross out any that don't work. As you proceed, the set of possibilities dwindle until you're left with only a few viable paths.

Here are the conditions for this puzzle (also listed in the video):

1. The raft needs at least one animal to paddle it across the river, and it can hold at most two animals.

2. If the lions ever outnumber the wildebeest on either side of the river (including the animals in the boat if it's on that side), they'll eat the wildebeest.

3. The animals can't just swim across, and there are no tricks; the animals have to use the boat as described.

Tune in to see how it's done:

For more on this puzzle, check out this TED-Ed page which explains its relationship to the The Missionaries and Cannibals Problem.

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The Simple Optical Illusion That Makes an Image Look Like It's Drawing Itself
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Artist James Nolan Gandy invents robot arms that sketch intricate mathematical shapes with pen and paper. When viewed in real time, the effect is impressive. But it becomes even more so when the videos are sped up in a timelapse. If you look closely in the video below, the illustration appears to materialize faster than the robot can put the design to paper. Gizmodo recently explained how the illusion works to make it look like parts of the sketch are forming before the machine has time to draw them.

The optical illusion isn’t an example of tricky image editing: It’s the result of something called the wagon wheel effect. You can observe this in a car wheel accelerating down the highway or in propeller blades lifting up a helicopter. If an object makes enough rotations per second, it can appear to slow down, move backwards, or even stand still.

This is especially apparent on film. Every “moving image” we see on a screen is an illusion caused by the brain filling in the gaps between a sequence of still images. In the case of the timelapse video below, the camera captured the right amount of images, in the right order, to depict the pen as moving more slowly than it did in real life. But unlike the pen, the drawing formed throughout the video isn't subject to the wagon-wheel effect, so it still appears to move at full speed. This difference makes it look like the sketch is drawing itself, no pen required.

Gandy frequently shares behind-the-scenes videos of his mechanical art on his Instagram page. You can check out some of his non-timelapse clips like the one below to better understand how his machines work, then visit his website to browse and purchase the art made by his 'bots.

And if you think his stuff is impressive, make sure to explore some of the incredible art robots have made in the past.

[h/t Gizmodo]

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See If You Can Solve This Tricky Coin-Flipping Riddle
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Make sure your head is in working order before trying to solve this riddle from TED-Ed, because it's a stumper.

Here's the scenario: You're an explorer who's just stumbled upon a trove of valuable coins in a remote dungeon. Each coin has a gold side and a silver side, each with an identical scorpion seal. The wizard who guards the coins agrees to let you have them, but he won't let you leave the room unless you separate the hoard into two piles with an equal number of coins with the silver side facing up in each. You've just counted the total number of silver-side-up coins—20—when the lights go out. In the dark, you have no way of knowing which half of a coin is silver and which half is gold. How do you divide the pile without looking at it?

As TED-Ed explains, the task is fairly easy to complete, no psychic powers required. All you need to do is remove any 20 coins from the pile at random and flip them over. No matter what combination of coins you choose, you will suddenly have a number of silver-side-up coins that's equal to whatever is left in the pile. If every coin you pulled was originally gold-side-up, flipping them would give you 20 more silver-side-up coins. If you chose 13 gold-side-up coins and seven of the silver-side coins, you'd be left with 13 silver coins in the first pile and 13 silver ones in your new stack after flipping it over.

The solution is simple, but the algebra behind it may take a little more effort to comprehend. For the full explanation and a bonus riddle, check out the video from TED-Ed below.

[h/t TED-Ed]

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