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Trick brain teasers appear difficult at first, but they have a trick that makes them really easy.


Puzzle ID:#50001
Fun:*** (2.13)
Difficulty:*** (2.71)
Submitted By:eighsseAus******
Corrected By:eighsse




Sam and Lisa live in a city in the desert of Nevada, USA, whose altitude is equal at all points, and whose streets run perfectly north-to-south and east-to-west. They are at the intersection of Harrison Street, which is north-south, and Jefferson Street, which is east-west. They are both walking to an intersection that is a few blocks east and a few blocks south from where they are now. They both take direct routes, using only two streets each (and therefore making only one turn each), but Sam takes Harrison Street while Lisa takes Jefferson Street. Assuming that neither encounters any obstacles, and that the turns take the same distance to complete, is there any reason why Sam's path or Lisa's path could be considered longer than the other's?


Earth is not flat.

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Nov 20, 2013

Excellent Work!

Sorry, no balloons or confetti for you; you missed them by one!
Nov 20, 2013


And *shakes fist at you!*
Dec 02, 2013

I got so confused by this
But good teaser!
Dec 02, 2013

Thanks anyways hehe. Were you confused just by the reasoning, or by my actual explanation of the setup? Because, it's a really simple setup but I could have probably explained it better.
Dec 22, 2013

Most boring teaser I have seen yet!!
Dec 22, 2013

Oh yeah, I forgot, deep thinking is boring. My bad ;)
Dec 22, 2013

Actually, Lisa's path was longer. Reason= She had been drinking and was staggering back and forth.
Dec 22, 2013

@cutebug: Haha, very well
Dec 22, 2013

The first thing I noticed was the category; trick.
"Harrison Street, which is north-south, and Jefferson Street, which is east-west."
Typically in the US streets run east and west and avenues run north and south.
Dec 22, 2013

Street name guidelines vary a lot. It doesn't seem, based on my research that I did for this teaser, that things like that are followed too strictly in most places. Good thinking, but it wasn't what I was going for
Dec 22, 2013

This is less a "trick" teaser, than one that depends on a knowledge of spherical geometry. And indeed, there is another answer, which does make the teaser a "trick," to wit: Lisa's path is a bit longer because "Jefferson Street" is comprised of more letters, and hence is longer, in that sense, than "Harrison Street."
Dec 22, 2013

I personally think it's pretty tricky. The idea is, the minds of most people, even if they have a good understanding of spherical geometry, will not think about that, because road maps are projected so that road grids look precisely square, and because the effect of the curvature is never an issue because it is extremely small.
Dec 23, 2013

Another more likely cause for one of the routes to be longer by a larger margin is that one of them may have walked along a street that has a hill while the other walked along streets that were flat.
Dec 23, 2013

@dsjt: You're absolutely right, that is a much more likely cause. In fact, I thought of that too, but unfortunately, it was after submitting this teaser that it crossed my mind. I have already submitted the correction, but I haven't had any corrections be approved since I joined Braingle several months ago... so I dunno if it will be done.
Jul 21, 2014

The difference you've pointed out is comfortably under a millimeter -- I'll bet its a few microns. It is WAY more significant that the person going east, then south is somewhat less likely to have to step around a stop sign than the person going south then east.

In any case, the extra up and down they would travel due to one sidewalk being broken and the other not would totally swamp your difference.
Jul 21, 2014

Agreed zag, but the point is that it takes some thought to even realize that this makes ANY difference at all, whether significant or infinitesimal. Granted it is irrelevant to the practicality of something like taking a walk... But when you consider that, for certain destinations, it could make you take an unnecessary trip 180 degrees around the equator... that's a big deal. In this teaser, it doesn't add up to anything, but the point is the fact itself, not the practical effect.
Dec 10, 2016

The effect of the Earth's curvature on that scale is extremely small. 1 cm of error on the part of the road-paving crew dwarfs it, and is thus a better answer.

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