Knight's task

Relevant wiki: Chess Puzzles

To reach g2 safely, the knight must take the white bishop at a8. To be able to take that bishop, it must take the white bishop at d8. To be able to take that bishop, it must take the rook at g8. We cannot take either of the knights (without being attacked first) so we must simply avoid them, and it turns out that the pawns are irrelevant.

The least possible number of moves from d2 to g8 is 3 (d2-e4, e4-f6, f6-g8), but this sequence of moves is not possible, since f6 is attacked by a bishop. It must take more than 3 moves to take the rook. Since getting from d2 to g8 involves a change of square colour, it must take an odd number of moves. It is possible to get to g8 to take the rook safely in 5 moves (d2-f1, f1-e3, e3-f5, f5-h6, h6-g8), and so the least number of moves to take the rook safely is 5.

We now need to get from g8 to d8 safely. The only safe first move is g8-h6.To get from h6 to d8 requires an even number of moves (same square colour) and the only way of doing this in two moves (h6-f7, f7-d8) is not safe, since f7 is attacked by a knight. Thus it must take at least 5 moves to get safely from g8 to d8. The move from g8 to d8 can be done in 5 safe moves (g8-h6, h6-f5, f5-g7, g7-e6, e6-d8). Thus the least number of moves to get from g8 to take the bishop at d8 safely is 5.

To take the bishop at a8 involves a change of square colour, so must take an odd number of moves, and cannot be done in one move. It can, however, be done in 3 moves (d8-e6, e6-c7, c7-a8). Thus the least number of moves to get from d8 to take the bishop at a8 safely is 3.

We now need to get from a8 to g2 safely. Thus must take an even number of moves (same square colour), and is too far to be done in two moves. It can be done in 4 moves (a8-b6, b6-d5, d5-e3, e3-g2). Thus the least number of moves to get from a8 to g2 safely is 4.

Putting these together, the least number of moves to get from d2 to g2 safely is $5 + 5 + 3 + 4 = \boxed{17}$ .

Relevant wiki: Chess Puzzles

To reach g2 safely we need to capture the bishop at a8 for which the bishop at d8 must be captured. In order to do so we must capture the rook at g8. Hence the following steps:

1. Nf1
2. Ng3
3. Nf5
4. Nh6
5. Nxg8
6. Nh6
7. Nf5
8. Ng7
9. Ne6
10. Nxd8
11. Ne6
12. Nc7
13. Nxa8
14. Nc7
15. Nd5
16. Ne3
17. Ng2

I guessed 0 and 5. Then my last answer, 17, was a 100% guess. Boom.

You move fist to capture the rook, then the bishop at d8 and lastly capture the bishop at a8 (because it guarding G2) and come back to G2 ,, all the while avoiding the two white knights. So 17 is right