Solution to: Big Numbers
The digits of the requested two numbers obviously form descending sequences. Furthermore, if you have two pairs of numbers with equal sums, the pair of which the numbers have the smallest absolute difference, is the one of which the numbers have the largest product. Using this knowledge, the two numbers can easily be constructed by placing the digits one by one, starting with 9 and ending with 1:
| 9 8 |
-> | 96 87 |
-> | 964 875 |
-> | 9642 8753 |
-> | 9642 87531 |
Conclusion: the requested two numbers are 9642 and 87531 (and the product of these two numbers is 843973902).
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