12*42=24*21
&
203313*657624=426756*313302
are the smallest and the largest samples I provide for
mirror multiplication
Please provide additional pairs.
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(ac)=b(fd)
examples:
122*884=488*221
662*133=331*266
(100a+10b+c)(10d+e)=(10e+d)(100c+10b+a)
implies
ad=ce and b=(aecd)/(ed)
[a,d,c,e must be chosen carefully]
example
682*13=31*286

Posted by Jer
on 20160731 20:59:54 