[ October 9, 2001 ]
How many palindromes can you find
that are the products of two pandigital numbers ?
|Two pandigital numbers|
1023687954 and 2901673548
which on their own defy all palindromicy
(any rearrangements of their digits never produces palindromes)
yet when multiplied together produce surprisingly this palindrome
There exists lots and lots more similar solutions.
Can you find them ? How many are there in total ?
Final score is 1277 [ January 2, 2009 ]
In collaboration with Peter Kogel.
I created a webpage twopan.htm where I display
all the palindromic products that we encountered.
Can you discover the first palindromes being the products
of three, four and more pandigitals ?
On [ April 20, 2012 ]
Carlos Rivera included the above 'three' question in his Puzzle 633
Soon after Giovanni Resta came with these smallest & largest solutions
1069458273 x 1082674593 x 1362840759
= 1577999653293663923569997751 
9540138762 x 9568170243 x 9743625018
= 889414381197666666791183414988 
Frank Rubin (email) wrote [ January 20, 2012 ]
I have found a 29-digit palindrome which is the product
of three 10-digit pandigital numbers.
2067945831 x 2758436091 x 3581704962
= 20431106772402320427760113402 
This took me about 100 hours of computer time to find.
I estimate that there are somewhere between 80,000 and 320,000
solutions, so there's no way I'm going to try to find them all.
If there is some interest, I might try searching for
the smallest solution.
Peter Kogel (email) wrote [ October 28, 2008 ]
So far the closest I have come to success are the following :
38766662887833033878826666783 = 1264358097 x 8257640913 x 3713063103|
37766638930788088703983666773 = 5769810243 x 8759416023 x 747259857
37766629851728882715892666773 = 2605894371 x 6291457803 x 2303563221
37766607369477677496370666773 = 1965024387 x 5610249387 x 3425767317
37766578522759495722587566773 = 1348296057 x 2659034781 x 10534122369
The problem is somewhat challenging to say the very least !
I began my search at a purely random point to test the efficiency
of my program and to try to gauge how long such a search might take.
Based on the progress I have made so far, I must confess that I'll
probably abandon the search, unless I can either think of a way
to radically improve the efficiency of my search algorithm or am
very lucky. I can see no reason why such a solution should not exist.
Perhaps one of your other readers can shed some light on the subject.
WONplate 97 investigated the ninedigital version of this topic !