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You make me laugh (Posted on 2015-07-28) Difficulty: 3 of 5

See The Solution Submitted by Ady TZIDON    
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Solution Analytic Solution | Comment 1 of 2
I started with taking each equation mod 10 to get:
E * E = T mod 10
S * T = E mod 10

This has 7 solutions: (E,S,T) = (2,3,4), (2,8,4), (3,7,9), (4,9,6), (7,3,9), (8,2,4), (8,7,4).

T takes only three values: 4, 6, 9. It is also the lead digit of TRUE.  IS and IT are close, so I made the assumption that sqrt(T*1000) < IS and  IT < sqrt((T+1)*1000).

If T=9 then I=9, a contradiction for an cryptarithm.  

If T=6 then I=7 or 8.  If I=7 then S and T are both large, only 8 or 9.  But no solutions match.  Similarly if T=8 then S and T are both small, 0 to 4.  Two (E,S,T) fit this: (2,3,6) and (8,2,6)  but for both of these the equation IS*IT=TRUE fails to work.

Then the only option is T=4.  Then I=6 and S and T are at least 4.  Two (E,S,T) fit: (2,8,4) and (8,7,4).  The second option fails but the first one works: IS*IT=TRUE is 68*64=4352.

Then to verify TRUST/RIRE = 43584/3632 = 12 = ME.  This is good, so I have the solution.

  Posted by Brian Smith on 2016-11-24 11:38:30
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