【One Day One Day】06 Intelligence Tests for the Re-examination of Postgraduate Entrance Examination

Sometimes accumulation is also a kind of wisdom.

  Here is the test record of the intelligence questions in the 2021 Harbin Institute of Technology Computer Postgraduate Entrance Examination for student Yang, which will be updated continuously.

1. Back to square one (February 24)

  How many points are there on the earth, one mile to the south, one mile to the east, and one mile to the north to return to the origin?
[Thinking]
  If it's not a special place, you definitely can't return to the origin. Then this point must be in a special place. We consider the equator ¹ , the south pole ² and the north pole ³ . Then let's consider the azimuth at the equator, the South Pole and the North Pole (some geographical knowledge is involved here, as shown in the figure below):

position	Orientation characteristics
equatorial	There are four directions of east, south, west and north
South Pole	Any direction pointed at this point is north
North pole	Any direction pointed at this point is south

  Then you can consider the South Pole and the North Pole:

[Answer]
  Going one mile south, one mile east, and one mile north can you return to the origin? Consider the following locations:

1. The South Pole and its nearby points are
     at the South Pole, all directions are north , then one mile to the south is to rotate in place, one mile to the east is to rotate in place, and one mile to the north at the south pole is It is the characteristic of walking one mile in any direction , while walking one mile north is one mile walking in any direction, and it is definitely not possible to return to the original point.
     Considering the points near the South Pole, notice that walking a certain distance east and west near the South Pole is a circular arc . If one mile to the east can return to the origin, then one mile to the south, one mile to the east, and one mile to the north is equivalent to walking one mile to the south and one mile to the north, so you might be able to go back. To the origin. To the east you can walk a mile back to square one , from the starting point (set point A) to the south a mile to reach the place (to point B) should satisfy: B point to the distance from the South Pole r = 1/2kπ (k为正整数)to point B One mile to the east is equivalent to circling the earth several times to return to point B, and then one mile to the north from point B to return to the original point.1+1/2kπAll points from the south poleAll are in line with the meaning of the question, and the distance they have traveled is shown in the figure below.
   
2. The North Pole and its nearby points are
     at the North Pole. Go 1 mile south, that is, go 1 mile in any direction . Suppose you reach point A, and go east at point A, which is actually walking an arc , assuming you reach B point. Then go north at point B, then go to the north pole, and you can return to the north pole (origin), soNorth poleIn line with the meaning of the question. The distance it traveled is shown in the figure below.
     At the point near the North Pole, as described above, find the point that can return to the origin by walking one mile east , that is, the point away from the North Pole 1/2kπ(set as point C). But at this point, one mile northward does not exist (going north 1/2kπto reach the North Pole, and then going north is to make a circle in place, so the final location is the North Pole. If it is the origin, the starting point is also the North Pole. Point, one mile south will not reach point C), so the points near the North Pole are not in line with the meaning of the question.
   

[Answer] The
  North Pole and 1+1/2kπ (k为正整数)all points away from the South Pole .
[Summary]
  This question is actually closely related to the cycle in the C language, that is, when the South Pole (North Pole) goes to a point other than North (South), it turns in situ , near the South Pole (Pole) Moving in the direction except east and west is walking around a circular arc, so it can be back to the original place , and its essence is a cycle.
  But to be honest, this question also requires high geographical knowledge, and it is indeed a difficult problem for science and engineering students with a poor geographical foundation.

2. Turn on the lights (February 25)

  There are 100stack lights, numbered 1~100, and the lights are all on at the beginning. Then perform the following operations in sequence:

1. Press all switches;
2. Press 2the switch numbered as a multiple of;
3. Press 3the switch numbered multiple of.

  Excuse me, how many lights are on at the end?

3. Direction (February 26)

  A disc is painted in black and white, each of which occupies a semicircle. The disc rotates at an unknown speed and in an unknown direction. Some color sensors are available. Ask how to use the least sensor to test whether the disk is rotating clockwise or counterclockwise? How many sensors should I use at least?

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1. Wikipedia _ equator ↩︎

2. Wikipedia_South Pole↩︎

3. Wikipedia_North Pole↩︎