Each different letter in the below matrix represents a different integer from 1 through 7, the same letter always representing the same integer. The product of all four numbers represented in a given row appears to the right of that row. The product of each column appears at the bottom of the column. Just to make things interesting, the rows and columns spell out words.
|
A
|
B
|
E
|
T
|
60
|
|
R
|
E
|
A
|
R
|
20
|
|
E
|
A
|
S
|
E
|
35
|
|
A
|
N
|
T
|
E
|
90
|
|
50
|
120
|
105
|
6
|
|
Find the value of each letter.
From Mensa Puzzle Calendar 2017 by Mark Danna and Fraser Simpson, Workman Publishing, New York. Puzzle for October 16.
The simultaneous alphametic equations:
T*R*E*E = 6, R*E*A*R = 20, E*A*S*E = 35, A*R*E*A = 50, A*B*E*T= 60, and A*N*T*E = 90 solves as:
T = 3, R = 2, E = 1, A = 5, S = 7, B = 4 and, N =6
Consequently, the required arrangement is given by:
-------------------------+
| 5 4 1 3 | 60
| 2 1 5 2 | 20
| 1 5 7 1 | 35
| 5 6 3 1 | 90
-------------------------+
50 120 105 6
*** I sincerely hope to posit an analytical solution in future.
Edited on May 14, 2022, 11:06 pm
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