MEDIUM + SIZE = HOUSES
What is this puzzle?
Solve the addition alphametic puzzle where MEDIUM + SIZE = HOUSES. Each letter represents a unique digit from 0-9. No number starts with zero.
Difficulty: hard · Category: addition · Unique letters: 9
This hard-level addition alphametic puzzle features 9 unique letters (D, E, H, I, M, O, S, U, Z). In the equation MEDIUM + SIZE = HOUSES, each letter maps to a distinct digit from 0 to 9. With only 9 of 10 digits used, 1 digit remains unused in the solution. The leading letters M and S and H cannot represent zero — this is your first constraint. To solve this efficiently, focus on letters that appear in multiple positions across the equation — these are the most constrained and often the easiest to determine first. 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 9 unique letters to determine.
- Leading letters: M, S, H. None of these can be zero.
- There are 9 unique letters, so 1 digits from 0–9 will not be used.
- Start from the rightmost column (units place) and work left, tracking carries between columns.
- With two addends, each column can produce a carry of at most 1.
- With many unique letters, use elimination and constraint tracking to narrow down possibilities step by step.