Letter-column addition
Assign distinct digits to A, B and C so a two-column addition is correct.
Logic & rule checking
- Players
- 1–4 cooperative
- Time
- 10–18 minutes
- Materials and quantities
- The printed AB + AC = BA puzzle and a digit trial log; pencil.
1–4 cooperative
Prepare
Use AB + AC = BA, where AB means the two-digit number ten times A plus B. A, B and C are digits 0–9, each letter always keeps the same digit, and different letters have different digits. A and B are leading digits, so neither may be zero; C may be zero.
Play
Try a digit assignment and write the ones-column sum B+C. Its last digit must be A; if it reaches 10, record a carry of 1 to the tens column. Then check A+A+carry=B. Do not choose a new value for a repeated A when it appears in another position.
Example
A=1, B=3, C=8 gives 13+18=31. Ones: 3+8=11, write 1 and carry 1. Tens: 1+1+1=3. All three digits are distinct and both leading digits are nonzero. Merely matching the units column would not suffice.
Finish
Find one fully checked assignment, then compare with the separate example key. This puzzle can have more than one valid assignment; the task is not to find a unique secret code. If searching for all assignments, enumerate the allowed distinct digits and preserve the leading-zero rules.
Adapt
Use large digit cards and a written carry box. One partner checks repeated-letter consistency and another performs the arithmetic. Start with the demonstrated numbers before replacing them with letters. There is no speed score.
Aim: Assign distinct digits to A, B and C so a two-column addition is correct.
Practice within this activity: Assign distinct digits to A, B and C so a two-column addition is correct.
Adult observation: Ask the participant to explain one legal choice. Accept passing and a partner writing; do not infer a lasting ability from a single round.
Mechanism and adaptation: A separately written PartyPageKit version of the mechanism described below, with original examples and materials. The earliest inventor is not established here.
Goals describe observable activity choices, not measured long-term gains or institutional endorsement.
Free alternatives: Write the three-letter equation and trial rows on scrap paper; no calculator is required.
Buying recommendations reserved; no purchase required.
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.
Player letter addition
Find one assignment: AB + AC = BA. Digits 0–9; different letters different digits; A and B nonzero. Keep the same digit for every copy of a letter.
+ AC
────
BA
| A | B | C | Carry |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Player column check
| Trial A/B/C | B+C units/carry | A+A+carry | Full equality |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Teacher instructions and checked example · separate
1–4 cooperative
The printed AB + AC = BA puzzle and a digit trial log; pencil.
Write the three-letter equation and trial rows on scrap paper; no calculator is required.
Print only the relevant player pages; keep this teacher page separate. Read the full web rules before leading. A helper may write or move pieces, and anyone may pause or pass. No classroom or physical-printer trial is claimed.
A=1, B=3, C=8: 13+18=31. Ones 3+8=11; tens 1+1+1=3. This is one valid assignment, not a uniqueness claim. Other distinct-digit, nonzero-leading solutions are accepted after full addition.