Can a knight move through all positions.. (Im new and someone asked me this as a riddle :3)

The board is clear, a knight stands at A8 (leftmost corner) with endless moves can you move the knight through all positions and then end on H1 (rightmost corner)

Other than brute forcing and testing every possibility and move... can I know the answer?

Yes.  A Knight's Tour covers every square of the board just once.

https://en.m.wikipedia.org/wiki/Knight%27s_tour

Moving from a8 through h1 and touching all the squares on the board without any restrictions on the number of repeated moves would just be a particular example of that calculation.

He needs to go through every position on the board...

Oh I see thank you, But I need to make sure the final move is at h1 and he starts at a8.... I see this has other sources so I will check in more details, thank you.

 Yes this can be done. 

DeirdreSkye, I think you don't understand the "riddle" because the original poster was not extremely clear. By "all positions" (perhaps not the best way to describe it) I think they meant: can you get the Knight to land on a1, a2, a3 ... h7 h8, translating to "can the Knight land on each of the 64 squares?" 

The answer is easy for a chess player, of course it can! As most players (certainly 1000+ rating) know, Bishops are restricted to their color while a Knight can reach any square (Knights "switch" color square they are on every move)

I know that many GMs practice with the Knights by similar drills. Such as this "riddle" or variants with certain immovable pieces on the board (like Kings or fixed pawns). However, I have never heard this as a riddle - only practice drills; in these drills, only one side moves (If your White, Black's pieces are fixed/pass the tempo without moving). The positions need not be legal - they are simply practice drills for Knight movements (why no Kings on the board is acceptable).

Yes, it can be done. The easiest way is to the let knight describe laps around the board (a8-c7-e6-g7 etc.), rather than just moving it about at random (when the knights tend to get trapped or locked out of a sole square somewhere).

Wow thanks everyone, This community is amazing! I need to get myself to play chess more :>

Post #2 mentions "Knight's Tour", but I am not so sure this is what the "riddle" refers to here IM pfren. The original post could have been perhaps a bit more clear; but after all, they are not really a chess player themselves  so you can't really expect great terminology and jargon (they simply posted on chess.com to answer this "riddle" given to them). I think they are simply asking "if a Knight can land on any of the 64 squares?" If this is the case then - clearly it is "yes"; if this was MY misunderstanding the meaning of this "riddle", then the answer may be "no." 

Many people may be overthinking this simple question. ???

It is not possible to complete a knight's tour on the same color square that you began on, since a knight's move always changes color, it would take an even number of moves to land on a square of the same color, but not including the starting square, there are 63 total moves, an odd number. If it's a re-entrant tour though, which means the knight ends on the same square it began ( the REAL knight's tour ), then it would "end" on the same color it began on.

I made that one myself actually with a practice site for it. It's SUPER easy, even the re-entrant one, using the quadrant systems method.

As an aside, decades ago George Koltanowski would give his Knight's Tour talk to various groups. Spectator's would write whatever they wanted in each of the 64 squares (drawn on a blackboard), and George would study the board for a few minutes.  Then he would turn his back on the board and someone would name a starting square.  He would then take a knight through the board, repeating what had been written in each square.  It was quite impressive.

26,534,728,821,064 is the number of CLOSED knight tours, the number of open tours is unknown.

FFS, I thought no-one was going to spot this. *takes hat off to pfren in silent thanks that he got here.*

Pfren's answer is correct for a true Knight's tour. but the question has a proviso: His question allows the N to visit the same square twice. 

I love Pfren's answer, but it isn't the correct answer to this particular question. 

Agreed, Pfren, which is why I love your answer. It presumed that the question was far more clever than it actually was.

I'm sorry I caused so much trouble... again, thanks for the help.

?

Yes

Long ago I had a chess teacher from Leningrad who turned the board over so the playing surface couldn't be seen and he wanted me to tell him how many moves it takes a knight to go from h8 to a8. It was blindfold chess. After I thought about it a little while I told him 5 moves.

He said ok. Now tell me which squares u used to get there! I did.

Fun times.