Knight-visit tour

Visit all twenty-five squares once using a long-two, short-one jump.

Shape & spatial thinking

Players: 1–4 cooperatively
Time: 15–20 minutes
Materials: A 5×5 numbered route grid, one marker and a 25-step log.

Prepare

Label a 5×5 board A–E and 1–5. Start at A1 and write 1 there. The aim is to visit each square exactly once, ending anywhere; returning to A1 is not required. Use a pencil trail or one marker with a numbered log, not a chess set. No square is blocked.

Play

A legal jump changes one coordinate by two and the other by one, in either direction. From A1 the only destinations are B3 and C2. Intermediate squares are irrelevant: a jump does not pass through or visit them. You cannot make a side-step, diagonal step or jump to a square already numbered.

Worked example

The prefix A1,B3,A5,C4,E5 is legal: each consecutive difference is one-by-two or two-by-one, and all five locations differ. It is not a complete solution. Before moving, point to both coordinate changes, then add the next number. A helper may check without suggesting the next destination.

Finish and check

Success is a verified sequence of twenty-five distinct legal squares. If stuck early, keep the log as an attempt, then erase one last number at a time to explore another branch or reset. Backtracking is allowed for practice but not counted as a new forward visit. Stop after three attempts or twenty minutes, with no promise every chosen prefix can be completed.

Adaptation and limits

The host sheet includes one fully checked route. Keep it separate and reveal only a next step if requested. Drawing connecting lines may cross, which is allowed; visiting a square twice is not. Enlarge the labels or dictate coordinates for a partner to record. This exercises route checking, not a measure of chess strength.

Purpose, observation and provenance

Within this activity: Visit all twenty-five squares once using a long-two, short-one jump.

Name a legal action, record the changed state and explain the check. One session does not measure lasting ability.

Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.

Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.

Paper size

Rules to keep beside the materials

Label a 5×5 board A–E and 1–5. Start at A1 and write 1 there. The aim is to visit each square exactly once, ending anywhere; returning to A1 is not required. Use a pencil trail or one marker with a numbered log, not a chess set. No square is blocked.
A legal jump changes one coordinate by two and the other by one, in either direction. From A1 the only destinations are B3 and C2. Intermediate squares are irrelevant: a jump does not pass through or visit them. You cannot make a side-step, diagonal step or jump to a square already numbered.
The prefix A1,B3,A5,C4,E5 is legal: each consecutive difference is one-by-two or two-by-one, and all five locations differ. It is not a complete solution. Before moving, point to both coordinate changes, then add the next number. A helper may check without suggesting the next destination.
Success is a verified sequence of twenty-five distinct legal squares. If stuck early, keep the log as an attempt, then erase one last number at a time to explore another branch or reset. Backtracking is allowed for practice but not counted as a new forward visit. Stop after three attempts or twenty minutes, with no promise every chosen prefix can be completed.
The host sheet includes one fully checked route. Keep it separate and reveal only a next step if requested. Drawing connecting lines may cross, which is allowed; visiting a square twice is not. Enlarge the labels or dictate coordinates for a partner to record. This exercises route checking, not a measure of chess strength.

Knight-visit tour — play materials

Visit	Coordinate
1
2
3
4
5
6
7
8
9
10
11
12
13

Visit	Coordinate
14
15
16
17
18
19
20
21
22
23
24
25

Host check — keep private until finished

Host route is generated and independently checked in the material key. Prefix A1,B3,A5,C4,E5 is legal, not a full-tour claim.

A1 → C2 → E1 → D3 → E5 → C4 → A5 → B3 → C1 → A2 → B4 → D5 → E3 → D1 → B2 → A4 → C5 → E4 → D2 → B1 → A3 → B5 → C3 → E2 → D4

These are model answers or legal examples, not records of an experiment or learner outcomes.

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