It is probably the most famous alphametic in mathematical recreation: a verbal sum that looks like a toy and ends up functioning as a chain deduction.
SEND MORE MONEY
Riddle statement
A young mathematician, son of a mathematician, writes to his father to ask for money, but decides to do it his own way. Instead of writing the amount directly, he sends him this sum:
Each letter represents a different digit from 0 to 9, and no word can start with 0.
How much money does he send?
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Solution
Since the sum of two four-digit numbers produces a five-digit number, necessarily M = 1.
In the thousands column, when adding S + M plus the possible carry, the result ends in O and generates that new initial figure. This forces O = 0 and, for the carryover to occur, S must be the highest figure available: S = 9.
From there, the central columns chain the carryovers in a very restrictive way, discarding incompatible assignments one by one. The only solution that satisfies all columns is:
S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2
This gives:
The parent sends you exactly 10652.