Each different letter in the below matrix represents a different integer from 1 through 8, 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.
|
E
|
L
|
M
|
S
|
360
|
|
M
|
O
|
A
|
T
|
70
|
|
M
|
A
|
M
|
A
|
100
|
|
A
|
M
|
E
|
N
|
240
|
|
150
|
280
|
150
|
96
|
|
Find the value of each letter.
From Mensa Puzzle Calendar 2021 by Fraser Simpson, Workman Publishing, New York. Puzzle for June 17.
(In reply to
Puzzle Answer by K Sengupta)
I looked for an alternate way of solving this puzzle and decided to sidestep the analytic avenue for this instance.
The simultaneous cryptarithmetic equations:
E*L*M*S=360, M*O*A*T=70, M*A*M*A=100, A*M*E*N=240, E*M*M*A=150 and, L*O*A*M=280
solves as: (E,L,M,S,O,A,T,N)=(3,4,5,6,7,2,1,8)
Now, M*A*M*E=5*2*5*3=150 -> Checks out to be accurate.
S*T*A*N= 6*1*2*8=96 -> Accurate
Accordingly, the completed array is as follows:
3 4 5 6
5 7 2 1
5 2 5 2
2 5 3 8
### I hope that I will soon be able to posit an independent analytic solution of my own.
Edited on April 13, 2022, 2:25 am
Online Solver based Puzzle Answer
