Cryptarithm - Tribute to Bob Marley
In the multiplication problem below, each digit has been replaced by a
letter. Can you determine the value of each letter?
B O B
× B O B
-------------
M E O Y
M I L O
M E O Y
-----------
M A R L E Y
B × B = Y,
so possibilities there are
B Y
2 4
3 9
4 6
7 9
8 4
9 1
(For B = 0, 1, 5, or 6, B × B ends in the same digit, but Y must be different.)
O × B = O (O ≠ 1 since O × BOB ≠ BOB)
B O
2 x
3 5
4 x
7 5
8 x
9 5
(The only multiples of 2, 4, or 6 which end in that same digit are 1 and 5,
which are already eliminated.)
O = 5, B is odd
O + O = E ( + 10 ?) (the O in the first MEOY, and in MILO, and the E in MARLEY)
So, E = 0.
B Y O E
3 9 5 0
7 9 5 0
9 1 5 0
Next is M, from B × BOB:
B Y O E M
3 9 5 0 1 (3 × 3 5 3 = 1059)
7 9 5 4 x (7 × 7 5 7 = 5299 - doesn't work)
9 1 5 8 x (9 × 9 5 9 = 8631 - doesn't work)
So B O B = 3 5 3 and we can work out the rest:
3 5 3
× 3 5 3
-------------
1 0 5 9
1 7 6 5
1 0 5 9
------------------
1 2 4 6 0 9
B = 3
O = 5
M = 1
A = 2
R = 4
L = 6
E = 0
Y = 9
I = 7
8 does not appear
