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It's early in the wee hours of the morning when a lonely farmer loads up his truck with his goods to sell. He lives far from the city and if he wants to ensure a good spot at the bazaar, he will need to leave with haste. The road is long and dull, the farmer sees but a single car driving in the other direction in the early morning mist during the first half an hour. After an hour has passed, the farmer looks out the window and sees the house of an old friend of his and notes to himself, almost as if to calm his own nerves: "I've already covered more than half of the way to the city. Surely I will make good sales today."

The day is hot and winding as the farmer calls people out to buy his goods. At long last when the sun has set, the farmer packs what little remains of his cargo and starts to travel back home. Lighthearted and in good mood, he can barely notice the time passing until he sees his friend's house again, saying to himself, "Oh my, I've already covered more than half the way! Surely I can get home early today."

The farmer drove with the same speed both in the morning and in the evening. How is it possible that he had passed more than half the way on both times when reaching his friend's house?

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    $\begingroup$ This is the first time I'm asking a question on this site, so pardon if I'm not that spot on with tagging. $\endgroup$
    – Etheryte
    Apr 26, 2015 at 11:16
  • $\begingroup$ because it's a different friend's house? $\endgroup$
    – Vincent
    Apr 26, 2015 at 11:18
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    $\begingroup$ @VincentAdvocaat Quoting the question, "he sees his friend's house again", it's the same house. $\endgroup$
    – Etheryte
    Apr 26, 2015 at 11:19
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    $\begingroup$ Not having the rep to answer I have to leave this as a comment: The highway is divided and the two parts take different routes through some very rugged terrain because there's only space for one lane in many places. He can only see his friend's house from different vantage points on the two paths. $\endgroup$
    – Loren Pechtel
    Apr 27, 2015 at 17:46
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    $\begingroup$ Now that an answer has been accepted, I'm sure the question is sensible and can upvote it! :-) (It's often hard to tell with this type of puzzle.) $\endgroup$
    – Rand al'Thor
    Apr 27, 2015 at 19:15

8 Answers 8

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On both occasions, when the farmer sees his friend's house he is

looking backwards.

This is a short and simple solution and seems to match everything stated in the puzzle.

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  • $\begingroup$ Simple yet very elegant, +1 $\endgroup$
    – Vincent
    Apr 26, 2015 at 11:35
  • $\begingroup$ This is one of the occasions where you found an even better answer than the original answer, therefore I'm accepting your answer as the correct one. $\endgroup$
    – Etheryte
    Apr 27, 2015 at 11:21
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    $\begingroup$ If the farmer is looking back then he has passed his friend's house not reached it. Hasn't he? $\endgroup$
    – Gareth BoxRoom
    Apr 27, 2015 at 13:22
  • $\begingroup$ @GarethBoxRoom If you read the OP carefully, it only says he sees his friend's house, not that he's reached it. There's nothing in either case to say where he's seeing it from. $\endgroup$
    – Rand al'Thor
    Apr 27, 2015 at 19:14
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    $\begingroup$ But at the end it says "when reaching his friend's house" $\endgroup$
    – Gareth BoxRoom
    Apr 27, 2015 at 21:25
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enter image description here

It's because the farmer drove along different roads. The road was two-way for the first half an hour, then became one-way.

In the picture, the red color represents the morning road, the blue color shows the evening road. The green box is his friend's house.

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    $\begingroup$ From the question: "[..] the farmer sees but a single car driving in the other direction in the early morning mist during the first half an hour." While not explicitly said, he takes the same road home. But this is a good guess. $\endgroup$
    – Etheryte
    Apr 26, 2015 at 11:29
  • $\begingroup$ @Nit Check my updated solution! $\endgroup$
    – leoll2
    Apr 26, 2015 at 11:38
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    $\begingroup$ That looks like a map of Boston! $\endgroup$
    – Milo Brandt
    Apr 26, 2015 at 16:50
  • $\begingroup$ This works, and you're rather close to the original answer of the question, good work! $\endgroup$
    – Etheryte
    Apr 27, 2015 at 11:28
  • $\begingroup$ @Nit: could not the roads have diverged into one-way streets after he saw the car? Or perhaps he took the different route just for the lols? $\endgroup$
    – geometrian
    Apr 28, 2015 at 7:13
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For completeness sake, I'll add the original answer to the puzzle as an image:

The friend's house is at the red dot, it doesn't really matter at which side of the road. The traffic in the below image is right-handed, if it was left-handed, just flip the image.

Explanation image

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  • $\begingroup$ This is much more similar to my answer than rand al'thor's one. Why did you choose to accept his? (I'm just asking, I'm not greedy of reputation). $\endgroup$
    – leoll2
    Apr 28, 2015 at 11:50
  • $\begingroup$ @leoll2 See the comment on his answer. $\endgroup$
    – Etheryte
    Apr 28, 2015 at 12:39
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Because the bazaar was not in the city he referred to the first time he passed his friend's house. The bazaar is beyond the city. You want us to assume that the bazaar is in the city, but you never explicitly say it is.

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  • $\begingroup$ This is the most clever and believeable of the solutions so far, I think. $\endgroup$
    – JLee
    Apr 26, 2015 at 22:11
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    $\begingroup$ Seems in line with what I first thought: He was more than halfway to the entrance of the city, but the bazaar is farther into the city. $\endgroup$
    – DoubleDouble
    Apr 27, 2015 at 16:32
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The most natural answer is this one:

He started further away than his house at the start of the day. Suppose he lives on a large farm, and his goods are stored at the far end of the farm, whereas the house is at the end closest to the city. Now, if the friend's house is just a little short of half way between his house and the city (as viewed from his house), then starting from his storage, his friend's house is a little over half way to the city. On the way home, his friend's house is a little over half way to his house.

For a visual sense of what's happening...

S---H------------------------F--------------------------C
Distance from Storage to Friend's house: 28
Distance from Friend's house to City (or back): 26
Distance from Friend's house to Home: 24

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  • $\begingroup$ Was trying to work this one out myself, but I see someone already beat me to it. $\endgroup$
    – Zibbobz
    Apr 27, 2015 at 20:17
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This is because:

Between the friend's house and his own house is a weight-limited bridge (or even a height-limited tunnel). For example, the route avoiding the bridge is 100 km from home to his friend's, and from his friend's home to the city is 80 km. However, after selling all his goods at market to make his vehicle lighter (or less tall), he can take the weight-limited bridge, cutting the distance from his friend's to home to 50 km.

This explains the market aspect better than others, IMO, but I don't know the significance of:

the farmer sees but a single car driving in the other direction in the early morning mist during the first half an hour

This seems like a clue...

EDIT: Perhaps the mist is a clue:

Due to the morning mist, the bridge is closed to traffic, regardless of vehicle weight, so he has to take a detour.

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  • $\begingroup$ While this is good speculation, it relies on things that aren't related to the story at all. $\endgroup$
    – Etheryte
    Apr 27, 2015 at 11:26
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The long road is dull because it is lined by identical houses exactly 1 mile apart, that is, except for the friend's house whose neighbours are 2 miles away in each direction. So Mr Farmer doesn't recognize his friend's house until he has driven 1 mile past it.

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  • $\begingroup$ He'd recognise the house 1 mile before reaching it when coming from either direction. $\endgroup$
    – Ken Y-N
    Apr 27, 2015 at 8:25
  • $\begingroup$ As commented on the question, it's the same house. $\endgroup$
    – Etheryte
    Apr 27, 2015 at 11:24
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Because his friend lives in a van/car, and has moved during the day.

Perhaps he came from the city to cheat on the farmer with his wife, while he was away.

So they basically met at different spots each time. First time closer to the city, second time closer to the farm.

(Though this doesn't tell how the farmer knows it's more than halfway thorugh)

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