Here is a puzzler that recently came up on Car Talk:
A man and a woman go for a walk. During the entire duration of that walk, they walk side by side, never further than a foot apart from each other. None of them ever gets ahead of the other.
When the walk is over, the woman says “I walked four miles”. The man says “I walked five miles”.
The Car Talk guys gave one solution and I came up with two additional ones.
Can you find them? And maybe new ones?
#1 by Ravi on December 12, 2010 - 7:40 pm
The woman is walking in a circle with radius 4 feet
The man is walking in a circle with radius 5 feet
they are always at a distance of 1 feet
and they make 840.76433 rounds each
#2 by Sri Atluru on December 12, 2010 - 7:40 pm
The mathematical solution:
The women is walking on a circle of radius 4 feet. The man is walking on a circle with radius 5 feet. They make 840.76433 rounds and then stop. Total distance covered by woman and man is 4 miles and 5 miles respectively.
#3 by Sri Atluru on December 12, 2010 - 7:48 pm
Since, there is no constraint on the velocity or time of either participant, it can also be assumed that the women is at the center of a circle of radius 1 feet. And the man is a point on the circumference. While the women moves in a straight line for 4 miles, the man moves around the women at variable speed so that he travels a distance of 5 miles.
#4 by rrpai on December 12, 2010 - 7:49 pm
They are on 2 conveyor belts/exercise m/c parallel 1 feet, moving at 4/5 miles/h respectively. They walk so that they are stationery wrt ground, but effectively walking 4/5 miles.
#5 by Ron on December 12, 2010 - 7:51 pm
a) 2 treadmills
b) dude walks 1+x steps forwards and x steps back for each 1 step the lady takes
b’) dude orbits the lady while they walk
#6 by Corey on December 12, 2010 - 7:52 pm
Other possible solutions: 1) the man and woman are on side-by-side treadmills going different speeds. 2) the woman’s path is level, while the man’s path rises and falls such that he walks an extra mile.
#7 by Brett Porter on December 12, 2010 - 8:03 pm
They could do about 840 laps of a circular track with a radius of 4 feet for the woman, 5 feet for the man 🙂
Or more likely they could be on adjacent treadmills going at different speeds.
#8 by Sebi on December 12, 2010 - 9:03 pm
The woman is walking in a straight line but the man is walking in a wavy line in such a way that he gets closer and further from her but never more than 1 foot away.
#9 by Daniel Spiewak on December 12, 2010 - 9:04 pm
I was going to suggest the circle solution mentioned by several others, but it occurs to me that there is a much simpler answer: one or both of the distances are false. As they say, if you start with an invalid premise, you can prove anything!
#10 by rrpai on December 12, 2010 - 9:52 pm
soln #2
man at A and woman at B begin at 1 feet separation. Woman walks straight. Man moves in a angle and at end of walk they converge to a point C. Think of it as a triangle with vertices ABC,
AC=5 (hypotenuse), BC=4 (adjacent side), such that
angle(ACB) = cosinv(4/5)
#11 by rrpai on December 12, 2010 - 9:58 pm
oops my above soln may not work i think as for a triangle a+b > c (4+1=5 and it cant be that) 😛
#12 by Mark on December 13, 2010 - 1:00 am
The woman has a dog called “four miles” and the man has a dog called “five miles”.
#13 by Paul on December 13, 2010 - 1:13 am
I straight away thought of the circle and treadmill answers. But what about:
* They walked 5 miles. The man, however, was a time-travelling Irishman from the 17th century and used Irish miles (6720 feet). So he walked 5.1 miles and was just rounding down
* The woman got a thorn in her foot and, while trying to get it out, hopped for a mile or so. She didn’t count the hopping as distance ‘walked’.
or something equally silly…
#14 by Imre Lumiste on December 13, 2010 - 1:36 am
A few more ideas:
1) these are obviously rounded distances, they might have used different algorithms to round their distance (eg. floor vs ceiling)
2) the man, being a true gentleman, takes the slippery side of the pavement
3) the woman measures in irish miles, while the man uses english miles
4) a nice evening ends in a nasty argument
5) the woman is talking about distance between start and finish, while the man is talking about distance along the actual path
6) they might be talking about distance walked during a longer period of time (e.g. the whole week), not just the walk described in the puzzle
7) they use different measuring / estimation methods for distance (e.g. GPS vs time spent multiplied by usual average speed)
8) one of them has invalid data for estimating distance (e.g. GPS lost signal, clock has run out of batteries)
#15 by Ben Tilly on December 13, 2010 - 4:40 am
One more solution that nobody else has come up with.
The man walked a mile to the woman’s house before they began walking together.
#16 by Rafa? Dowgird on December 13, 2010 - 5:06 am
Simple solution: at least one is lying.
#17 by Gill Bates on December 13, 2010 - 5:26 am
Please refrase the problem in the form of a question. This isn’t Jeopardy.
#18 by JNevill on December 13, 2010 - 5:55 am
I love the dog walking solution. That is the winner. No doubt!
@Gill_Bates “What are things a moron says while spelling fuh-net-ik-lee”
#19 by Guess_Who? on December 13, 2010 - 8:57 am
Actually the correct sentence are:
“I walked four, Miles”
“I walked five, Miles”
Miles is the driver, and they´re talking about steps:
The man has bigger legs…
Crazy shit, yeah I tried…
#20 by Achllies on December 13, 2010 - 12:51 pm
The dog solution is by far the winner.
Combining the dog and the friend solution.
I walked four, Miles.
I walked five, Miles.
Both are dog trainers and are telling their friend Miles, the number of dogs they walked today.
#21 by Craig Tataryn on December 13, 2010 - 12:54 pm
I was thinking the the woman’s path is level in elevation and the man’s path is riddled with 2,640 1-foot hills he has to go up and down
#22 by rrpai on December 13, 2010 - 7:51 pm
4 people, man, woman, “four miles”, “five miles”
man – i walked, “four miles” (to “four miles”)
woman – i walked, “five miles” (to “five miles”)
#23 by Youssef on December 14, 2010 - 8:05 am
Ok, here is another one.
The women was upset, and the man tried to pleases her , every time he tried to do so she pushes him back 1 foot away then he keeps trying. 🙂
#24 by Tarun K on December 22, 2010 - 7:15 pm
@Cedric,
what’s your answer?
~T
#25 by imp on December 29, 2010 - 1:44 pm
Men exaggerate and Women can’t tell where they’re going.