perplexus.info :: Numbers : Mirror multiplication

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

Please provide additional pairs.

No Solution Yet Submitted by Ady TZIDON

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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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