It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery draw and handed her pen and paper. But the fairy told him that these were 6 wishes and that thus it was not possible for her to tell him. Instead she wrote one number on the paper and said: "This is the sum of all of next week's numbers in the lottery draw." Markus then thought There are too many possibilites for me to just guess the numbers. The fairy, who had sensed his thoughts then gave him another tip: "The number of possibilites that this sum can be achieved multiplied with it is a really big number, in the magnitude of a few million $(number >= 10,000,000)$, and it is also equal to the product of the six numbers." After she had vanished, Markus began to scribble and sure enough, won the lottery the next week.
What are the six numbers?
The solution is unique.
- Six distinct numbers between including 1 and 49 - for you maths people: $[1,49]$
- Sum of these times possibilities of summands is equal to product of these numbers and >= 10,000,000.