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

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

 No Solution Yet Submitted by Ady TZIDON No Rating

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 To cooperate | Comment 7 of 8 |
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)

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 non-valid 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 2016-08-01 03:45:24

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