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Double pandigital number divisible by 11

Published on Sunday, 30th November 2014, 10:00 am; Solved by 1720;
Difficulty rating: 20%

Problem 491

We call a positive integer double pandigital if it uses all the digits 0 to 9 exactly twice (with no leading zero). For example, 40561817703823564929 is one such number.

How many double pandigital numbers are divisible by 11?