2
$\begingroup$

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

$\endgroup$
1
  • 2
    $\begingroup$ I can confirm that rot13(gurer vf bayl bar fbyhgvba). $\endgroup$ Nov 28 '20 at 15:14
3
$\begingroup$

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:

$2916 / (2\times 9\times\ 1\times 6) = 6219 - 6192$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.