One-stroke house: rules and printable materials

Trace every required edge once without lifting the pencil; crossing lines do not create extra junctions.

Suggested group

1–8

Plan for

8–15 minutes

Bring

Graph sheet and pencil

Read the graph correctly

The diagram is a house with five labelled corners. A is lower left, B lower right, C upper right, D upper left and E the roof peak. Required edges are AB, BC, CD, DA, DE, EC, AC and BD. The two diagonal lines cross inside the square, but there is no dot there, so you cannot turn at that crossing. Only the five labelled dots are junctions.

State the exact objective

Choose a start dot. Draw along all eight required edges exactly once without lifting the pencil. Revisit a dot whenever necessary, but do not retrace an edge, add an edge or jump between unconnected dots. Passing through the same dot twice is allowed; using the same segment twice is not. Finishing somewhere other than the start is permitted.

Plan before tracing

Give one sheet to each person or pair and allow two minutes to plan with a finger. A recorder may write a proposed list of letters before anyone traces. Use a fresh graph for each serious attempt so overlapping failed routes remain readable. If a mistake is noticed, stop that attempt and discuss it; do not turn a broken line into an extra legal edge. There is no need to race.

Worked checks

The partial route A–B–C–D uses AB, BC and CD. A later move D–B is allowed because BD is a different, unused edge. However, B–A would reuse AB and invalidate that attempt. Moving from the centre crossing to C is not a legal instruction because the centre is not a vertex. The edge checklist helps distinguish repeated corners from repeated edges.

Hints and solution

The first hint asks players to count lines touching each labelled dot. A second hint says to try starting at A or B. One full answer is A–B–C–D–E–C–A–D–B. Tick the eight edge names as that route is followed; each must occur once. A reverse route is also valid, and the host should accept any route that passes the same tests. Stop after ten minutes and let players request the answer sheet. For younger guests, first demonstrate an easier two-edge path without changing the printed house during a scored attempt.

Printable materials

Preview before printing at 100% scale; turn off browser headers and footers. Keep host answers separate. This is a manual tabletop kit, not computer opposition or an automatic judge.