Red-side view: files a-i left to right, ranks 0-9 bottom to top; river between 4 and 5.
Complete, original sparse teaching positions under ordinary movement and general-safety rules. No claim of reachability from an opening, competition-history legality, engine strength or professional review.

P01: One friendly screen
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 rH, b7 bR
Proposal: b2 to b7.
Answer: Yes. Red captures the black chariot on b7.
The occupied points strictly between b2 and b7 are b4 rH only. Red’s horse is a valid screen. Move the red cannon to b7 and remove the black chariot there; keep the red horse on b4. Red’s general on e0 is not exposed by the resulting position. There are fewer total pieces after a capture, but the screen itself survives.

P02: Adding a second screen
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 rH, b6 bC, b7 bR
Proposal: b2 to b7.
Answer: No. There are two screens: b4 and b6.
This starts from exercise 1’s arrangement and adds a black cannon at b6. Both b4 rH and b6 bC are strictly between b2 and b7. Their different colours do not cancel each other. A cannon capture needs exactly one screen, so leave the initial position unchanged. “At least one screen” is the wrong test.

P03: Removing the only screen
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b7 bR
Proposal: b2 to b7.
Answer: No. Zero screens cannot support this capture.
The destination b7 still contains a black chariot, but b3, b4, b5 and b6 are all empty. A cannon may move through an open line to an empty destination; it cannot use that ordinary movement to capture the enemy chariot. Removing a screen can therefore stop an attack instead of improving it. Keep both pieces on their original intersections.

P04: An enemy cannon can be the screen
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 bC, b7 bR
Proposal: b2 to b7.
Answer: Yes. The black cannon on b4 is a valid screen and remains there.
There is exactly one intervening piece, b4 bC. A screen can belong to the opponent and can itself be a cannon. Red captures only the black chariot on b7. The enemy cannon on b4 is not removed as part of that capture; there is no chain capture. General safety also passes on this listed position.

P05: A friendly destination stays unavailable
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 rH, b7 rR
Proposal: b2 to b7.
Answer: No. Red cannot land on the red chariot at b7.
There is one screen, b4 rH, but b7 contains a friendly destination piece. The screen rule does not allow a cannon to capture its own side, stack with another piece or push it elsewhere. Record this as a friendly-destination failure. It is different from an incorrect screen count, even though both prevent this proposal.

P06: One screen, but no piece to capture
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 rH
Proposal: b2 to b7.
Answer: No. A cannon cannot jump a screen to an empty destination.
The only intervening piece is the red horse on b4, and b7 is empty. There is no enemy at the landing point to capture. An ordinary cannon move needs a clear route, so b4 blocks this move. Having exactly one screen does not make every landing beyond it available; first identify the destination type.

P07: An open ordinary move across the river
Red to move. Pieces: e0 rG, f9 bG, b2 rC
Proposal: b2 to b5.
Answer: Yes. Red moves quietly from b2 to empty b5.
The intermediate intersections b3 and b4 are empty. The destination b5 is also empty, so this is a non-capturing move with zero screens. It crosses the river between ranks 4 and 5 without changing the cannon’s movement rule. Both generals remain safe and no piece is removed. Compare this with exercise 3’s open line to an occupied enemy destination.

P08: A diagonal target does not make a cannon line
Red to move. Pieces: e0 rG, f9 bG, b2 rC, b4 rH, c7 bR
Proposal: b2 to c7.
Answer: No. b2 to c7 is not an orthogonal cannon move.
The proposed destination differs in both file and rank. Do not trace a bent route or count the horse on b4 as if it established a diagonal jump. A cannon’s source, screen and captured destination must lie on one straight rank or file. The marked diagonal line is only the rejected proposal; leave all original pieces unchanged.

P09: A capture route that exposes facing generals
Red to move. Pieces: e0 rG, e9 bG, e3 rC, c3 rH, a3 bR
Proposal: e3 to a3.
Answer: No. Moving the cannon exposes facing generals.
The horizontal route e3 to a3 has one screen, c3 rH, and an enemy chariot at a3. That passes the cannon capture geometry. But e3 is the only occupied intersection between Red’s general on e0 and Black’s general on e9. Moving the cannon away clears the e-file and leaves the two generals directly facing. Reject the move for general safety; do not label the diagram as a completed legal capture.

P10: A legal capture gives check, with a legal reply
Red to move. Pieces: e0 rG, f9 bG, f2 rC, f4 rH, f7 bR, f8 bH
Proposal: f2 to f7.
Answer: Yes. Red captures on f7 and gives check, but this is not checkmate.
Between f2 and f7, the only screen is f4 rH. The black horse on f8 lies beyond the destination, so it does not count for this capture. After Red’s cannon lands on f7, that horse becomes the single screen between the cannon and Black’s general on f9: Black is in check. Black can reply with the horse f8 to h9 through the empty leg g8. Removing the f8 screen makes the f7-to-f9 line have zero screens; the general is no longer under that cannon attack. The reply stays on the board and leaves Black’s general safe.

CANNON MOVE-CHECK RECORD
Fixed Red-side view: files a-i left to right; ranks 0-9 bottom to top.
Position ID and side to move:
Every occupied intersection, including both generals:
Proposed cannon source and destination:
Same rank or file? Both endpoints on board and different?
Destination: empty / friendly / enemy (piece and side):
Occupied intersections strictly BETWEEN the endpoints:
Screen count and rule needed for this destination:
Tentative resulting board: cannon location / captured destination / retained screen:
Own general safe after the move? Facing-generals line or other attack:
If the opponent is in check, a tested reply (not a guessed mate claim):
Result and exact reason:
Competition rules or repetition history that still needs checking: