Brain Teasers
Maze Girl
A treasure is hidden in the middle of a maze. Each step is 1 m. The person starts at the entrance of the maze. She travels at 3 km's per hour. She starts facing north.
She takes 4 steps forward, then turns right. She then takes 2 steps and turns 45 degrees northwest. She then walks until she is exactly north of where she began. She then turns 90 degrees to her right, then walks in that exact direction until she is directly north of where she first turned 45 degrees. She then turns and faces directly north. She walks twice as far as she has already walked and turns left. She then walks a 1/4 as far as she has walked at an angle of 45 degrees. She then turns north and walks twice as far as she has previously walked north. She then turns right and takes 9 steps. She picks up the ruby and walks the same distance she has previously walked in the maze, but instead she continues walking east. After she walks this far, she sits down on a bench in the maze and is arrested. How long did the girl spend walking in the maze until she was arrested? She walked twice as fast after she got the ruby. Answer in seconds.
She takes 4 steps forward, then turns right. She then takes 2 steps and turns 45 degrees northwest. She then walks until she is exactly north of where she began. She then turns 90 degrees to her right, then walks in that exact direction until she is directly north of where she first turned 45 degrees. She then turns and faces directly north. She walks twice as far as she has already walked and turns left. She then walks a 1/4 as far as she has walked at an angle of 45 degrees. She then turns north and walks twice as far as she has previously walked north. She then turns right and takes 9 steps. She picks up the ruby and walks the same distance she has previously walked in the maze, but instead she continues walking east. After she walks this far, she sits down on a bench in the maze and is arrested. How long did the girl spend walking in the maze until she was arrested? She walked twice as fast after she got the ruby. Answer in seconds.
Hint
After she walks two paces northwest, she walks another two paces northeast because she does not turn north after walking two paces northwest.Answer
4m + 2m + (2m x tan 45 degrees) + (2m x tan 45 degrees) + 20m + 1m + 48m + 9m + 88 = 176 m. 88 m at 3 km per hour = (1/((3km/0.088km)) x 3600) = 105.6 seconds.Double the speed = 105.6/2 = 52.8 seconds.
Time spent in maze = 158.4 seconds.
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If I understand the question correctly, I don't believe the answer is correct. The walk to the northwest is along the hypotenuse of a triangle with legs of 2 meters, so it is longer than you determined. I therefore got a longer time (164.35 seconds)
This teaser is fraught with errors. depending on the assumptions i had to make, i received varying results from 161s to 178s. An exercise in tedium.
I think that this is an incorrect Brain Teaser and there are parts that can vary with the way you think it means...
I wrote this question and take full responsibility for my carelessness, concerning the angle of 45 degree's that shouldn't be found using tan but with using cos. The correct answer can be derived by doing the first two steps the same, then finding the length she walked at 45 degree's by dividing 2 m by the Cos of 45 degree's. By using this the answer will change from 158.2 seconds to the more correct answer of 163.8219474 seconds as I see it.
Not so much a teaser as a tedious math problem. However, I have yet a different answer than any above:
4 N
+
2 E
+
sqrt(2^2 + 2^2) NW
= sqrt( 8 ) NW
~ 2.83 NW
+
sqrt( 8 ) NE
+
2 * (6 + 2*sqrt( 8 )) N
= 12 + 4*sqrt( 8 ) N
~ 23.3 N
+
.25 * (2*sqrt( 8 )) W
= .5*sqrt( 8 )
~ 1.41 W
+
2 * (4 + 12 + 4*sqrt( 8 ))
= 2 * (16 + 4*sqrt( 8 ))
= 32 + 8*sqrt( 8 )
~ 54.6
+
9
= 59 + 14.5*sqrt( 8 )
~ 100.0 m to the ruby
@ 3000 m / 3600 s
= 5/6 m/s
6/5 s/m * (59 + 14.5*sqrt( 8 )) m
= 70.8 + 17.4*sqrt( 8 ) s
~ 120.0 s
+ 6/10 s/m * (59 + 14.5*sqrt( 8 )) m
= 35.4 + 8.7*sqrt( 8 ) s
~ 60.0 s
for a total time of 106.2 + 26.1*sqrt( 8 ) seconds, which is approximately 180.0 seconds or 3 minutes.
4 N
+
2 E
+
sqrt(2^2 + 2^2) NW
= sqrt( 8 ) NW
~ 2.83 NW
+
sqrt( 8 ) NE
+
2 * (6 + 2*sqrt( 8 )) N
= 12 + 4*sqrt( 8 ) N
~ 23.3 N
+
.25 * (2*sqrt( 8 )) W
= .5*sqrt( 8 )
~ 1.41 W
+
2 * (4 + 12 + 4*sqrt( 8 ))
= 2 * (16 + 4*sqrt( 8 ))
= 32 + 8*sqrt( 8 )
~ 54.6
+
9
= 59 + 14.5*sqrt( 8 )
~ 100.0 m to the ruby
@ 3000 m / 3600 s
= 5/6 m/s
6/5 s/m * (59 + 14.5*sqrt( 8 )) m
= 70.8 + 17.4*sqrt( 8 ) s
~ 120.0 s
+ 6/10 s/m * (59 + 14.5*sqrt( 8 )) m
= 35.4 + 8.7*sqrt( 8 ) s
~ 60.0 s
for a total time of 106.2 + 26.1*sqrt( 8 ) seconds, which is approximately 180.0 seconds or 3 minutes.
It helps if you know that a square has a diagonal sort(2) time its side. Then the trip to the ruby takes 50 + 29xsqrt(2) = 91 steps. Then time is 91/5/6 + 91/5/3 = 819/5 = 163.8 seconds.
Don't need trig. Don't need a lot of that incidental calculation.
The bit about walking as far as walked at 45 degrees is ambiguous. I guessed you meant obliquely to the compass axes. The wording could be a lot better.
Don't need trig. Don't need a lot of that incidental calculation.
The bit about walking as far as walked at 45 degrees is ambiguous. I guessed you meant obliquely to the compass axes. The wording could be a lot better.
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