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Saturday, July 26, 2008

Big Numbers

Using the ciphers 1 up to 9, two numbers must be made. The product of these two numbers should be as large as possible. All ciphers must be used exactly once.

The Question: Which are the requested two numbers?

Answer: The ciphers 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 ciphers one by one, starting with 9 and ending with 1:

9 96 964 9642 9642
-> -> -> ->
8 87 875 8753 87531

Conclusion: the requested two numbers are 9642 and 87531.

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