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Mirror multiplication (Posted on 2016-07-31) Difficulty: 4 of 5
12*42=24*21
&
203313*657624=426756*313302

are the smallest and the largest samples I provide for
mirror multiplication

Please provide additional pairs.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts Some algebra | Comment 5 of 8 |
It doesn't seem there are obvious extensions but here's how to generate some smaller equations:

(10a+b)(10c+d)=(10d+c)(10b+c)
implies ac=bd as in the first example.  Others include
14*82=28*41
13*93=39*31

(100a+10b+c)(100d+10e+f)=...
Implies
ad=cf and e(a-c)=b(f-d)
examples:
122*884=488*221
662*133=331*266

(100a+10b+c)(10d+e)=(10e+d)(100c+10b+a)
implies
ad=ce and b=(ae-cd)/(e-d)
[a,d,c,e must be chosen carefully]
example
682*13=31*286

  Posted by Jer on 2016-07-31 20:59:54
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