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They aren't ordering it. Let's use a much simpler thing, the pair of numbers is 1-4. That gives us only 10 possible combinations. The product person says they don't know the answer. What do we know? So if I told you the product of two numbers (positive integers) was 3, you immediately know 3 is prime and therefore the numbers are 1,3. Therefore either they cannot say they don't know if they were told 3. We can go through every combination and find what possibilities they could be. Well, it cannot be 1,1 or 1,2 or 1,3 because those produce products of 1, 2 and 3 because they don't have any other pair that can generate them. The same is true of 2,3 which is the only way to get six or 2,4 the only way to get 8. And 3,3 or 3,4 which are the only way to get 9 and 12. And lastly 4,4 is the only way to get to 16. You'll note that this is almost all pairs which is easy to iterate over by making the second number greater than or equal to the first. The only pairs left are 1,4 and 2,2 both of which produce a product of 4. So we, as the sun person, now know the product must be four. Given the product and the sum, we can deduce that it's 1,4 because we were told the sun was 5. When it goes to 100, it's the same process. Except now I have to iteratively eliminate pairs until there is only one solution. |