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Both Players uses 8 Knights on this chessboard game : The Knight Checker. All pieces starts in Rank 1 relative to players. White to move first. The Knight pieces makes regular moves as in a chess game rule. They can capture or tackle opponent piece and moves in any direction. To win one knight of any player must touchdown or move to Rank 8 first (or capture on rank first) without being captured by opposing knight. Also to win by capturing all opponents pieces. enter image description here

Is it possible that a games ends in a draw? That is , Black or White can not force a win.

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  • $\begingroup$ Do you know the answer to this question? $\endgroup$
    – Gareth McCaughan ♦
    Commented Aug 11, 2018 at 14:33
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    $\begingroup$ I'll play it some more with my neighbor maybe there is a draw. We use all pawns for the knights since we don't have 4 chess sets. $\endgroup$
    – TSLF
    Commented Aug 12, 2018 at 11:38
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    $\begingroup$ It seems like the sort of thing where either there's some fairly simple observation that solves it or the only way to solve it is some kind of exhaustive search taking millennia of computer time. $\endgroup$
    – Gareth McCaughan ♦
    Commented Aug 12, 2018 at 11:59
  • $\begingroup$ maybe when 2 computers play this game they end with a draw on game 1 $\endgroup$
    – TSLF
    Commented Aug 12, 2018 at 13:31
  • $\begingroup$ Assuming an end game situation where the a white knight (vs 3 pieces) try to touchdown,but prevented to by 3 black knights thus ends in repeating moves where that is considered a draw. Now I wonder if that is the only possible situation. $\endgroup$
    – TSLF
    Commented Aug 13, 2018 at 17:39

1 Answer 1

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I know this is a late answer, but I think I may have something!

enter image description here

Reasoning:

The draw is 1. Nf6 Ne7 2. Nd7 Ng6 3. Nf6 Ne7 4. Nh7 Ng6, etc.

White is forced into this. He can't move to g5 on turn 1 because of 1.....Nc3 with an unpreventable touchdown on b1. On Nf8, Nxf8 (assuming Evargalo's comment is correct) puts an end to that. So White must play 1. Nf6. Now, White is threatening to touchdown on g8. The only piece that can reach g8 is the Ng6, so Black plays 1..... Ne7, preventing the goal. Now, White has two choices that threaten a touchdown- d7 or h7. (If White doesn't threaten a touchdown, Black can play Nc3.) Either way, Black must play Ng6 to prevent the touchdown on f8. Now, the Na4 is guarding b6, White can't play his knight there, so to threaten a touchdown, White must play Nf6. Black must play Ne7, and the cycle continues, until a three-move repetition!

TL;DR:

A draw is possible, in the above position.

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