12*42=24*21
&
203313*657624=426756*313302
are the smallest and the largest samples I provide for
mirror multiplication
Please provide additional pairs.
Following the method of Jer, to just get samples, it is possible to simplify choosing some numbers as 0
F. ex:
(a*1000+b*100+c*10+d)*(e*1000+f*100*g*10*h)=
(h*1000+g*100+f*10+e)*(d*1000+c*100*b*10*a)
leads to:
dh=ae
hc+gd=af+be
ag+bf+ce=hb+gc+fd
Choosing c=f=0
dh=ae
gd=be
ag=hb
Three equations six variables
I choose: a=2 e=8 b=1
dh=16
gd=8
2g=h
These are dipendent. Really we have:
dg=8
2g=h
So can choose g=1 g=2 g=4 (g=8 result in nonvalid h values)
Get: a=2 b=1 c=0 d=(8, 4, 2) e=8 f=0 g=(1, 4, 8) h=(2, 4, 8)
Then:
2102*8048=8408*2012=16916896
2104*8024=4208*4012=16882496
2108*8012=2108*8012=palindrome with middle * or as you want to call it.
Edited on August 1, 2016, 4:00 am

Posted by armando
on 20160801 03:45:24 