Prove that for every point
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
on the surface of a regular tetrahedron there exists a point
![M'](/media/m/f/f/8/ff8b045c71a5c47d10ca08150706243e.png)
such that there are at least three different curves on the surface joining
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
to
![M'](/media/m/f/f/8/ff8b045c71a5c47d10ca08150706243e.png)
with the smallest possible length among all curves on the surface joining
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
to
![M'](/media/m/f/f/8/ff8b045c71a5c47d10ca08150706243e.png)
.
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Prove that for every point $M$ on the surface of a regular tetrahedron there exists a point $M'$ such that there are at least three different curves on the surface joining $M$ to $M'$ with the smallest possible length among all curves on the surface joining $M$ to $M'$.