xjo weekend zoomba lounge, page-85

Jeeper is a big boy! You are completely correct since Chris45 hasn't mentioned about the size of the tent.
You can make a tent that covers the whole Earth! LOL
It's a matter of investment?

Anyway, the coordinates of a location of the Earth are continuous.
By adjusting your tent size, if you pitch your tent at any locations excluding any places where its latitude, θ, between 89.91^°S and 90^°S because you are not able to go 10 km further south (as soon as you arrive at the south pole, you will see only north), you will arrive back at your tent fallowing the instruction .

Considering the radius of the Earth, R_E = 6371 km, and your journey ∆y = 10.00 km to south and then ∆x = 10.00 km to west and then 10.00 km to north,
if the size, L, of the tent (from its east end to west end) satisfies, you will always arrive back to your tent (initial starting position is the east end of the tent for convenience):

L =

cosθ cos(θ− θ0)

∆x

where

θ0 =

∆y 111.2

= 0.0899°

i.e.,

L =

cosθ cos(θ− 0.0899)

10.00 km

As you will expect, at the north pole (θ=90^°), even L=0, i.e., a sizeless tent satisfies your question but you will not able to sleep. Of course, at the north pole, any tents regardless their size will be enough to arrive back at your tent.

If the size of tent is considered, the number of locations that satisfies your conditions of journey is infinite since the location of your ideal Earth sphere is a continuous coordinate system.

This question is a year 10/11 level in Australia.

Hope good profits to all XJOers.