Sometimes, challenging puzzles have surprisingly straightforward solutions. This is one of those puzzles.

**Sunday Puzzle #20: The Monk And The Mountain**

* At precisely 7:00 a.m., a monk sets out to climb a tall mountain, so that he might visit a temple at its peak. The trail he walks is narrow and winding, but it is the only way to reach the summit. As he ascends the mountain, the monk walks the path at varying speeds. Though he stops occasionally to rest and eat, he never strays from the path, and he never walks backwards. At exactly 7:00 p.m., the monk reaches the temple at the summit, where he stays the night.*

* The following morning at 7:00 a.m. sharp, the monk departs the temple and begins his journey back to the bottom of the mountain. He descends by way of the same path, again walking slowly at times and quickly at others, stopping here and there to eat and drink and rest, but never deviating from the path and never going backwards. Twelve hours later, at 7:00 p.m. on the nose, the monk arrives back at the foot of the mountain.*

*Is there any point along the path that the monk occupied at precisely the same time on both days? How do you know?*

*If you're in need of a clue, click **here**.*

We'll be back next week with the solution â€“ and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. As always, be sure to include "Sunday Puzzle" in the subject line!

*Top image by Tara Jacoby*

### SOLUTION To Sunday Puzzle #19: Six Matches, Four Triangles

Last week, I asked you to create four identical, equilateral triangles using six matchsticks of equal length.

I received a number of correct responses, including several that I had not anticipated. Among the unanticipated answers was this one from commenter Platypus Man, who supplied a solution that gave not four equilateral triangles but *eight *(six of which were identical), plus a hexagon for good measure:

Some of you noted that arrangements like this one require that the matchsticks be placed *on top* of one another, such that the ends of the matches do not join together and therefore do not form complete triangles. While technically correct, I'm inclined to accept solutions that require criss-crossing matches as valid, given the way I posed the puzzle, which should have been more specific (more on that in bit).

Now, the solution I was *expecting*, which does not require the matches to cross one another, was the one submitted by commenter zheng3 and several others:

It's a regular tetrahedron! A polyhedron with six edges of equal length (our six matches) meeting at four vertices to form four equilateral triangular faces. It's the same shape as a four-sided die, as commenter D1g1taL0ne noted soon after the puzzle was posted.

This is the solution I was looking for. But if we count criss-crossing configurations like the one above, it is not the only valid solution. If I had wanted the tetrahedral solution to be the only solution, I should have been **more specific** with my phrasing when I first posed the puzzle. Instead of saying "using six matchsticks of equal length, create four identical, equilateral triangles," I should have said "using six matchsticks of equal length x, create four identical, equilateral triangles with side length x." Posed this way, the puzzle forces you to utilize all three dimensions.

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## DISCUSSION

No matter how the 2 paths wiggle, they

mustcross at some point. Therefore, yes, he will be at the same point at the same time, somewhere on the path.