3) Six Impossible Things Before Breakfast

Here I will post a series of (mostly) simple challenges to amuse you in the run-up to Christmas. I'll try to post one each weekday.
DDRM
Posts: 398
Joined: Mon 02 Apr 2018, 18:04

3) Six Impossible Things Before Breakfast

Post by DDRM »

During his summer break, Santa heard about the “What Three words” location system, where the whole earth is mapped into 3 metre squares, and has decided to use it for his deliveries this year. Making the following 6 “impossible” assumptions, work out the length of his route:

1) Pi is exactly 3
2) The world is a perfect sphere of radius 6300 km
3) Each “square” is indeed exactly 3 metres square (i.e. 3 metres on each side)
4) The “squares” are arranged in a helical pattern, starting at the north pole and finishing at the south pole, such that you can move from one square to the one immediately to its east, and cover the whole route.
5) He doesn’t have to worry about time zones to make all his deliveries at night
6) He can return to the north pole by following a line of longitude at 0 metres altitude

As a bonus, where should he go for breakfast? (Possibly obscure “literary” reference)

DDRM
Posts: 398
Joined: Mon 02 Apr 2018, 18:04

Re: 3) Six Impossible Things Before Breakfast

Post by DDRM »

Code: Select all

      @%=&0F0F
      PRINT "The surface area of a sphere is 4 x PI x R^2"
      PRINT "Here we are given PI = 3, and R = 6.3 million metres"
      PRINT "We need to divide this up into 3 x 3 metre squares, so each has an area of 9 m^2"
      PRINT "The distance betwen the centres of each adjacent square is 3 metres, since they are 'horizontally' aligned!"
      PRINT "So the total distance on the outward journey is:"
      PRINT "((4 * 3 * 6.3E6 * 6.3E6) / 9) * 3 metres. Cancelling a few 3's, we get 4 * 6.3E6 * 6.3E6 metres,"
      way_out_man%%=4*6.3E6*6.3E6
      PRINT "which is ";way_out_man%%;" metres, or "; way_out_man%%/1000;" km."
      PRINT
      PRINT "For the return journey, he will trace half a circumference of the earth, which is (2 * PI * R) / 2,"
      way_in_man%% = 3 * 6.3E6
      PRINT STR$(way_in_man%%) + " metres, for a total of "; (way_out_man%% + way_in_man%%)/1000;" km."
      PRINT "Note that the return journey is negligible in contrast to the spiral path!"
      PRINT
      time_s% = (way_out_man%% + way_in_man%%)/3E8
      time_hrs% = time_s% / 3600
      PRINT "Since the speed of light is about 3E8 m/s, he could get the journey time down to ";time_s%;" seconds, which is ";time_hrs%; " hours."
      PRINT "Sounds like this isn't going to be a viable strategy if the deliveries need to be done in one 'night'..."
      PRINT
      PRINT "Oh, and 'If you've done six impossible things this morning, why not round it off with breakfast at Milliways,"
      PRINT "the Restaurant at the End of the Universe?'"