Recover Hidden Digits from Carries
In a partly blanked addition, subtraction, multiplication, or long division, the missing digits are deduced column by column from the lowest place up, using how carries and borrows must propagate. The same cryptarithm logic deepens from three-digit sums to multi-digit products and division. It trains airtight place-value bookkeeping.
grade 3–4 Base-ten numbersOperations Work BackwardsEliminate Possibilities
Progression (5)
g3 1. Recover hidden digits using regrouping Base-ten numbersOperations
g3 2. Recover missing digits from column carries Base-ten numbersOperations
g3 3. Deduce missing digits in a multiplication OperationsBase-ten numbers
g3 4. Fill long-division blanks from the known Operations
g4 5. Deduce hidden digits from the ones place up Base-ten numbers
Bridges to competition (9)
Reasoning problems that extend this idea toward competition:
Recover hidden digits in a vertical sum Logic
Cryptarithm digit deduction Logic
Complete the multiplication equation Number arrangement
Multiplication cryptarithm Logic
Multiplication synthesis challenge Logic
Cryptarithm: Letters Stand for Digits Logic
Recover Erased Multiplication Digits Logic
Recover hidden digits in long division Number arrangement
Solve a cryptarithm for each letter Logic