maths
posted by john on .
can you replace the stars with figures
****
x 3
______
*****
the whole calculation uses each of the digits 09 once and once only
the 4 figure number contains three consecutive numbers which are not in order. the third digit is the sum of 2 of the consecutive numbers
the 1st,3rd,and 5th figure of the 5 digit number are three consecitive numbers but again they are not in order. the second and forth digits are also consecutive numbers

Here's the bruteforce solution, which was produced using MS Excel in about half an hour  so probably not much use if you have show your working and use the clues to get to the answer. There are five solutions that use the digits 09 exactly once:
5694 x 3 = 17082
6189 x 3 = 20457
6918 x 3 = 20754
8169 x 3 = 24507
9168 x 3 = 27504
Of these, only the first has three consecutive digits in the fourdigit number (4, 5 and 6), and the third digit (9) is the sum of the first two of these. The other conditions fit also. You don't need to look at any fourdigit number less than 3333, since the product with 3 doesn't have five digits, so you've got 6666 numbers to check. Interesting that the other four solutions all have the same digits in various permutations. 
5694 x 3 = 17082