MAI is the square of ST.
And:
. . . . . A
M A I
--------------
. . . . . . .
. . . . . . .
. . E N . . .
-------------------
P R I N T E M P S
MAI is a perfect square with 3 distinct digits.
I cannot be 0 or 1, or S would be I or A instead of S.
MAI is thus limited to {169, 196, 256, 289, 324, 529, 576, 625, 729, 784}
But ST is √MAI so S is limited to {1,2}
But A*I ends in S; and both A and I are found in MAI.
The only squares which could be MAI which have digits A*I ending in a 1 or 2 is MAI = {289 or 576};
but 8*9=72, therefore S=2, but √MAI=ST = 17 so S=1=2.
S cannot be both so MAI cannot be 289.
What about MAI = 576? then √MAI = ST = 24; and 7*6=42
From this brief analysis, we know:
MAI is 576
M=5
A=7
I=6
S=2
T=4
The smallest and largest 6 digits numbers, which when multiplied by 576 yield a 9 digit number are 173612 and 999999; but they also must end in 7
So we only need to test 82639 possible choices for the top line 6 digit number; and for each there is only 1 choice for PRINTEMPS.
With the speed of modern computers, this doesn't really matter much, but it was fun.
btw, in French, MAI is May and PRINTEMPS is SPRING
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Posted by Larry
on 2024-10-21 11:48:09 |
a preliminary analysis to limit search
