102. Five cards. I have five cards with the digits $1,3,5,7$ and 9 on them. How can I arrange them in a row so that the product of the number formed by the first pair of cards and the number formed by the last pair of cards, minus the number on the middle card, equals a number composed of repetitions of the same digit? For example (see figure), 31 multiplied by 79 minus 5 equals 2444; the last number would fit us if the 2 in the first place were also the number 4.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-033.jpg?height=125&width=485&top_left_y=2142&top_left_x=794)

Obviously, there should be two solutions, since both pairs of cards - the first two and the last two - are arranged completely symmetrically.
102. The solutions are the numbers 39157 and 57139. In each case, the product of the numbers 39 and 57 minus 1 equals 2222.