magic cryptarithm
VV RE HR
AH VE RL
RV HE VR
This is a magic square with magic constant HEH.
If you order the letters according there values you get the hidden word.
Solution:
The magic constant is 3 times the central value.
Proof: Let s be the constant.
a b c
d e f
g h i
s = a+e+i = g+e+c = d+e+f = b+e+h.
Adding these four sums gives
4s = a+b+c+d+e+f+g+h+i + 3e
Further we have for the three rows
s = a+b+c = d+e+f = g+h+i
Subtracting these three sums gives s = 3e.
This gives the key equation
HEH = 3 * VE
Now H can be at most two.
As H == 3*E (mod 10) we have only two cases to try.
H E V R
1 7 5 9
2 4 -
The rest is easily filled in.
55 97 19
21 57 93
95 17 59
magic constant = 171
123579
HALVER
References:
Praxis der Mathematik 39:4 (1997) 153