# maths

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can you replace the stars with figures

****
x 3
______
*****
the whole calculation uses each of the digits 0-9 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

• maths -

Here's the brute-force 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 0-9 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 four-digit 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 four-digit 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.

• maths -

5694 x 3 = 17082

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