One-stick equation repair: rules and printable materials

Repair 6 + 4 = 4 by moving one digit segment, keeping the plus and equals signs fixed.

Players

1–6 cooperative

Plan for

10–15 minutes

Bring

Printed seven-segment digits, paper strips and pencil

Use paper segments safely

Arrange the equation 6 + 4 = 4 using the printed seven-segment reference. Digits use positions a across the top, b upper right, c lower right, d bottom, e lower left, f upper left and g middle. The reference defines exactly which segments make each digit. Use paper strips, not lit matches, food sticks or small sharp objects.

Move exactly one segment

Take one existing segment from a digit and place it in an unoccupied segment position of a digit. Both affected digits must be valid standard digits after the move; source and destination may be the same digit. Leave plus and equals fixed. Do not rotate an entire digit, create an inequality, invent a new symbol, add a strip or remove one from play.

Test a proposed change

Write the new equation and check both arithmetic and digit shapes. A true statement made with a malformed digit is not a solution. Moving the middle segment of the first six to its upper-right position converts 6 into 0. The equation becomes 0 + 4 = 4. This uses one strip, leaves both operators unchanged and gives three valid digits.

Offer useful hints

Keep the host key separate if players should solve independently. A first hint can say that the moved strip may stay within the same digit. A second can point to the first six without naming its final form. Participants may identify segment letters while a helper rearranges the strips. There is no time limit and no penalty for discussing a move before committing it.

Validate new puzzles

For another round, begin from a true equation in the same digit system, move one strip to make a false but well-formed equation, and challenge someone to reverse it. Keep a before-and-after key. A puzzle can have more than one solution; accept any change meeting every stated restriction. Do not reuse examples based on handwriting styles that differ from the supplied seven-segment font.

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.