World!Of
Numbers

WON plate
115 |


[ 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
2970408257528040792 .

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 [28]

9540138762 x 9568170243 x 9743625018
= 889414381197666666791183414988 [30]




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 [29]

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 !

A000115 Prime Curios! Prime Puzzle
Wikipedia 115 Le nombre 115














[ TOP OF PAGE]


( © All rights reserved )
Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com