Hi, my son was given a problem to solve, he is having a problem finding the answer...any help greatly appreciated. Problem is as follows:

1_._ x _._ = _ _.5 _

use numbers 2-9 to fill in the blanks. Since 1 and 5 are already used i figured that the rest of the numbers filled in the blanks but can not figure it out. again thanks




It is easy to program it. here is my program in C which gave me the only solution
186 x 39 = 7254.

If you can make sense of the code below, you will notice that it does not "think" at all.
It simply lists all the possible multiplications, then retains the only one with the desired properties, in less than a second. Humans do this much slower, but humans can think. The game is to see whether there are some clever ideas to reduce the large amount of case-checking. For instance, instead of listing 10000 possibilities, we need only restrict ourselves to the 7*6*5*4 = 840 ways of putting numbers from 9, 8, 7, 6, 4, 3, 2 in the first four slots. After that, we can reason that some numbers in the first or third slots has to be big enough because there has to be a carry in the thousands.
After that ...

All in all, how many clues can you find to reduce the amount of calculations?