Spoiler for solution

in general the largest number produced by multiplication is achieved when the two numbers are close together.

so we want a 4 digit and a 5 digit number.

a b c d e

* f g h i

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the largest first digit occurs when a and f are 9 and 8. since we want them to be close, its better for a to be 8 and f to be 9.

the second largest digit will be 2 + 9*b +8*g. the largest value occurs when b is 7 and g is 6.

this puts the max value at 8300000 aprox. the next largest digit is 7*6 +9*c +8*h. the max value occurs when h is 4 and c is 5.

you can continue. the final answer is: 9642 *87531.

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