### Brain Teasers

# Maze Girl

Math
Math brain teasers require computations to solve.

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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