I could only get one answer for the following alphametic. Can you confirm?
ETAS / (E * T * A * S) = SEAT - SATE
All 4 lettes are separate digits from 1 to 9.
ETAS, SEAT and SATE are 4 digit numbers
NO Programming please
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2$\begingroup$ I can confirm that rot13(gurer vf bayl bar fbyhgvba). $\endgroup$– risky mysteriesCommented Nov 28, 2020 at 15:14
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1 Answer
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Yes, confirmed, here is how:
The r.h.s. can be written $EAT-ATE = 100 \times E + AT - (10 \times AT + E) = 9 \times (EE - AT)$ so $9$ must divide the digit sum $A+E+S+T$. Also the smallest product satisfying this constraint is $1 \times 2 \times 6 \times 9 = 108$ so $ETAS \ge 972 \times (EE-AT)$, therefore $EE-AT$ must be single-digit. Hence $E=A+1$ and $EE-AT>E$, in fact, it must be $EE-AT=E+1$, thus $T=9$, and $9 \times A \times E \times S \times T < 1000$. This leaves only $1,2,6,9$.
It remains to verify:
$2916 / (2\times 9\times\ 1\times 6) = 6219 - 6192$
