UNDER + THE + UNITED = STATES
What is this puzzle?
Solve the addition alphametic puzzle where UNDER + THE + UNITED = STATES. Each letter represents a unique digit from 0-9. No number starts with zero.
Difficulty: hard · Category: addition · Unique letters: 10
This hard-level addition alphametic puzzle features 10 unique letters (A, D, E, H, I, N, R, S, T, U). In the equation UNDER + THE + UNITED = STATES, each letter maps to a distinct digit from 0 to 9. The leading letters U and T and S cannot represent zero — this is your first constraint. This puzzle has 3 addends (UNDER + THE + UNITED), making carry analysis more complex. Start from the rightmost column and work left, tracking carries between columns. This is a challenging puzzle that requires systematic use of carry analysis, parity checking, and elimination. Start by listing all constraints, then methodically eliminate impossible digit assignments.
- This addition alphametic has 10 unique letters to determine.
- Leading letters: U, T, S. None of these can be zero.
- All 10 digits (0–9) are used, one per letter.
- Start from the rightmost column (units place) and work left, tracking carries between columns.
- With three addends, each column can produce a carry of at most 2.
- With many unique letters, use elimination and constraint tracking to narrow down possibilities step by step.