Can you tell a human from a machine?
Alan Turing and the Imitation Game
Suppose you have a modified Turing machine that can predict the future -- it can only give you information about a week ahead of time.
So you want to test the machine, and ask the machine to give you the lottery numbers for the next drawing of the 6/49 lottery. The machine cannot give you 6 numbers at the same time. It cannot handle this.
So you ask for the sum of the 6 lottery numbers.
The machine gives you that number.
However, there's a very large number of possible combinations that yield this sum.
Then, the machine tells you: If figure out exactly how many possible number combinations there are (from 6 out of 49 numbers) to yield this particular sum, and then multiply this number with the sum it will yield a new number of around one million, and you will also get the same number if you multiply all 6 lottery numbers with each other.
The ball is in your court. The machine awaits.
You need to figure out those 6 numbers. Solve this problem.