If I take 5 integers and multiply them all together, what's the maximum number of them that can be negative and give a negative answer?
2 Answers
If all
Explanation:
A negative number multiplied by a negative number gives a positive answer.
As long as there is an ODD number of negatives being multiplied, the answer will be negative.
So, in this case, if
If
Consider the examples below using just ones.
The order of the negative numbers makes no difference.
5
Explanation:
When we have a positive number multiplied by a negative number, we get a negative number. For instance:
And when we have two negatives multiplying each other, we get a positive number:
And so with five integers multiplying each other, we'll get a product that is negative if we have an odd number of negative numbers:
And we'll get an even number if we have an even number of negative numbers:
And so the maximum number of negative numbers we can have multiplying each other is 5.