Question

Solve the algebraic expression where numbers are represented by letters.
No two letters have the same value.
ONE + TWO + FOUR = SEVEN
Let 0=3, T=6, F=9

Answer 1

ONE + TWO + FOUR = SEVEN
0=3, T=6, F=9, N/E/W/U/R/S- unknown
3NE+6W3+93UR=SEVEN -->
10203
+NE
+W0
+UR
=SEVEN
It is clear that S=1, E=0
N=3+R or N+10=3+R =>N=R-7 ---> (1)
and N+W+U= 9 or 10 or 19 or 20 ---> (2)
V can be 2, 3 or 4. 2 or 3 are excluded (sum of 3 numbers can't be 0, and can't be 10 as V=3 impossible as we have already O=3), so V=4
So far we have O=3, T=6, F=9, S=1, E=0, V=4, remaining numbers are 2,5,7,8
To satisfy (1) and (2) we have options: N=5, R=2, W=7 or 8, U= 8 or 7 (here only N=R+3 and N+W+U=20 options work, others don't).
we have now:
350+673+9382=10405
350+683+9372=10405