In this description of Epaminondas with puzzles at the bottom, what is the solution to the first puzzle?
The solution is for white to move their row of 3 one space forward. There are a bunch of possible moves for black but white can guarantee a win from all of them.
If black moves away from their back line:
If black moves their leftmost piece away from the line, then red pushes forward. Black is forced to use their remaining 2 to capture red, who captures again. Black can't capture the remaining piece.
This is similar to the situation with the rightmost piece:
If black moves the middle piece away, then they will have to reform the broken 2 in order to defend the back line. Red aims a phalanx there:
If black moves the middle piece to the side to avoid this diagonal phalanx, red goes too far away on the other side:
If black stays on the back line
If black is staying on the back line, then their first move cannot be to the left. Any distance to the left allows red to take the first capture and keep pushing to win. Thus black moves right. If black moves more than one space to the right, then they're too far away to defend from the single piece moving in. If black moves one space to the right, red forces the black row to capture their piece, lining up the black phalanx to be split in half: