# Puzzle: is the bike moving left or right?

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I think:

[spoiler]The bike is going left.

The longer you go along a straight line, the more â€śtogetherâ€ť a bikeâ€™s tire tracks will be.

Just from the right-most third of the puzzle, if you think of the bike as travelling from left-to-right, it looks like the bike is going fairly straight, but the tracks are diverging. If the bike is travelling the opposite direction, the tracks would start to converge until you hit the next sharp turn - and thatâ€™s exactly what I see.[/spoiler]

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I agree. The lower track on the right is of the front wheel, the upper is the rear. Moving from right to left they describe a predictable fishtailing behavior, which doesnâ€™t work in the other direction.

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And now, having peekedâ€¦

I see that the trail is muddy just to show the tracks, not necessarily muddy enough to slide and fishtail around. So even though I got the direction right, I have the wheels on the wrong tracks. Oh, well.

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Yeah,

I had the wheels right - the rear wheel follows the front wheel, so itâ€™s always going to be on the inside of every curve. They used different logic than I did, though, making theirs about the distances between the two tires, where mine was about the convergence of trajectories after a turn.

So Iâ€™m not sure if Iâ€™m right for a different right reason, or if Iâ€™m right for the wrong reason.

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â€śAlways on the inside of every turnâ€¦â€ť except the mud made me think we were supposed to be thinking slippery, so I had the rear wheel traveling outside after a certain point in every turn, like a motocross bike. I think you and I were both thinking trajectories, but my image involved a lot of drifting and fishtailing.

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This sounds harder than it isâ€“ as soon as you start drawing bikes on top of the tracks it becomes very easy to see the answer.

The front wheelâ€™s track will always be the longer one (though you donâ€™t need to know that as you can just try both).

If you put your pencil at any point on the back wheel track, and draw a straight line tangent to the track, then if youâ€™re going in the right direction, you will always hit the front wheel track and your lines will always be the same length. (Because the bike is a fixed length, and always parallel to the back wheelâ€™s heading).

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The bike is traveling from right to left.

The proof is that well, itâ€™s just my opinion, but COME ON, it clearly is.

In other news, Iâ€™m pretty proud of myself for having figured out the [spoiler] tag from first principles.

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Iâ€™m not too familiar with motocross, but wouldnâ€™t the tracks be a different width in a skid, since the wheelâ€™s going at least somewhat sideways?

Plot twist - itâ€™s a unicycle!

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Yeah, probablyâ€¦ I didnâ€™t figure they were thinking that hard about such details!

Best effort after a few minutes of thought:

[spoiler]I believe the bike was traveling toward the left.

The front wheel of the bike can turn and steers, while the rear is fixed. If you were to plot the direction of travel of each wheel, the front leads the rear.

During a turn, the leading wheel also deviates farther than the rear wheel. The outside path is the front wheel.

Because the front wheel leads and deviates farther in a turn than the rear wheel, the two paths are closer to tangential at the start of a turn (as at right here), and closer to normal to each other at the conclusion of the turn (as at left here). The bike traveled to the left.
[/spoiler]

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Just to mess with youâ€¦

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To me what adds a layer of trickiness is that at higher speeds a two-wheel vehicle will countersteer (motorcycles at road speed) and the front wheel has to track slightly in the direction opposite of the turn to get the bike to lean over before the vehicle actually turns. At much slower speed, bicycles often do not countersteer.

Because the rear wheel cannot turn, the rear wheel always moves toward the front wheel.

Draw a tangent on the rear wheel curve and follow it forward to the front curve. As you move the point of tangency along the rear wheel curve the distance along the tangent line from the rear wheel curve to the front wheel curve that distance should be constant.

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My plot twist is that the person was riding a fixed gear bike backwards.

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Like a circle in a spiral, like a wheel within a wheel
Never ending or beginning on an ever spinning reel
As the images unwind, like the circles that you find
On the bicycle of your mind

Yeah, this seems one where gut instincts actually point to the right answer, and it only gets complicated if you try to approach it as a puzzle. Iâ€™m terrible at spatial reasoning, I wouldnâ€™t be able to think of it in the way they do in the answer. But as someone who has ridden a bicycle, it feels intuitive

Didnâ€™t Feynman show that the bike traveling to the left is the equivalent of an anti-bike traveling to the right, backward in time?

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Which bike arrived first?