## Task 2 - 320512

The largest six-digit number is sought, for which the following applies:

a) The number is even.

b) The tens digit represents a number three times as large as the ten-thousands digit.

c) The units and the thousands digit can be swapped without changing the six-digit number.

d) The hundreds digit represents a number half as large as the hundred-thousands digit.
After d), the hundred-thousands digit must be even; to make it as large as possible, one first tries to find a solution with eight and thus four for the hundreds place.

After b), the ten-thousands digit cannot be greater than three, so one tries to find a solution with the ten-thousands digit three and thus with the tens digit nine.

Since after a) and c) the same even digit stands in the units and thousands places, one tries to get the largest number by placing an eight in both positions.

The number 838498 obtained now satisfies conditions a), b), c), and d) and is, by construction, the largest possible.