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Pin Down a Number from Digit and Range Conditions

A hidden number is found by applying clues in turn — digit constraints, place-by-place comparison, and inequality bounds that fence the unknown into a finite range. Early versions narrow a four-digit number from digit clues; later versions bound an unknown digit or an unknown box value under a sum, product, or comparison constraint. The shared move is converting each condition into a restriction until one survivor remains.

grade 2–4 Base-ten numbersOperations Eliminate PossibilitiesMake a Systematic List

Builds on: Place-Value Regrouping

Progression (9)

g4 1. Compare numbers with an unknown digit Base-ten numbers · foundational
g4 2. Find a number from digit clues Base-ten numbers · foundational
g3 3. Bound an inequality at equality Operations · foundational
g3 4. Find a number satisfying product bounds Operations · core
g3 5. Bigger addend, bigger sum OperationsBase-ten numbers · core
g3 6. Estimate a product to solve an inequality Base-ten numbersOperations · core
g3 7. Estimate a product to bound an unknown Base-ten numbersOperations · advanced
g4 8. Build a number from digit conditions in order Base-ten numbers · advanced
g4 9. Compare place by place to bound an unknown digit Base-ten numbers · advanced

Bridges to competition (16)

Reasoning problems that extend this idea toward competition:

Build an equation meeting given conditions Number arrangement → Small-Domain Constrained Search
Numbers with swapped digit places Number arrangement → Small-Domain Constrained Search
Number satisfying sum and product clues Number arrangement → Small-Domain Constrained Search
Complete an arithmetic placement puzzle Number arrangement → Branching State Enumeration
Find unknowns satisfying multiple conditions Logic → Small-Domain Constrained Search
Find fractions meeting conditions Logic → Small-Domain Constrained Search
Find a Number Meeting Digit Conditions Number arrangement → Small-Domain Constrained Search
Deduce the hidden flipped cards Logic → Small-Domain Constrained Search
Numbers satisfying several conditions Number arrangement → Small-Domain Constrained Search
Insert plus and minus to make an equation Logic → Small-Domain Constrained Search
Arrange digit cards to hit a target number Number arrangement → Small-Domain Constrained Search
Insert plus or minus to make an equation true Number arrangement → Small-Domain Constrained Search
Deduce digits and place values from clues Logic → Small-Domain Constrained Search
Ascending, descending, palindrome numbers Number arrangement → Casework by Position / Vertex Type
Find numbers meeting digit clues Logic → Small-Domain Constrained Search
Find a number meeting given conditions Number arrangement → Small-Domain Constrained Search

Leads to competition types: Branching State EnumerationCasework by Position / Vertex TypeSmall-Domain Constrained Search