What numbers in the range up to 40000 are palindromes formed by the multiplication of a number and its reversal?
Let's require that the numbers being multiplied are not themselves palindromes because palindromic numbers when multiplied together always form palindromes. We find that only four numbers satisfy: 252, 20502, 23632, 26962 (see permalink). The details are shown in the table below:
The next number is 2005002 formed by the multiplication of 1002 and 2001. All the numbers being multiplied only consist of the digits 0, 1 and 2 as far as I can tell. For example, 40220902204 is a product of 200102 and 201002. There are no other starting numbers larger than 200102 in the range up to one million because of this restriction. Above one million, the first suitable number is 1000002 which multiplied by its reversal 2000001 produces the palindrome 2000005000002. In fact, any number formed from the digits 0, 1 and 2 (that does not end in 0) will produce a palindrome when multiplied by its reversal.
We can break away from this 0, 1, 2 restriction if we ask:
What numbers in the range up to 40000 are palindromes formed by the multiplication of a number and its reversal plus 1?
Well, once again, in the range up to 40000, there aren't many. In fact there are only 404, 575 and 737 (see permalink) with details shown in the table below.
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