There are 100 natural numbers, the sum of which is 2010. In these numbers, the number of odd numbers is less than that of even numbers. How many of these numbers are there at least?

There are 100 natural numbers, the sum of which is 2010. In these numbers, the number of odd numbers is less than that of even numbers. How many of these numbers are there at least?

Let's first look at the parity of numbers
When even odd numbers are added, sum is even
1+3=4
3+5+9+13=30
5+7+3+1+9+11=36
When odd numbers are added, the sum is odd
1+1+1=3
3+5+7+9+11=35
If an odd number plus an even number, the sum is odd:
1+2=3
4+5=9
7+8=15
241+246=487
The sum of several consecutive even numbers, no matter how many, is even
Since 2010 is an even number, it can be proved that it can be a continuous addition of 100 even numbers or a continuous addition of 100 odd numbers
But the least problem is that there are both even and odd numbers
In this way, we don't need to look at the number of 2010. We only need to use 100 now
To make the odd number and even number at least in 100, it is necessary to divide 100 by 2 and equal to 50, that is, 50 odd and even numbers each. But the topic requires even numbers to be more than odd numbers, so first put an odd number to the even side and turn it into 51 even numbers and 49 odd numbers. However, we also find that the sum on the even side is even numbers, the sum on the odd side is odd numbers, and the sum on both sides is odd numbers, which does not meet the requirements of the topic 2010
So put an odd number on the even side and turn it into 52 even numbers and 48 odd numbers. Even number plus even number equals even number, which is in line with the meaning of the question
Then look at the least odd number, as long as these odd numbers add up to even numbers, so at least two
Note: the questions asked are the least of the two different situations, not the same situation (don't be so stupid that they are wrong if they don't add up to 100)
Therefore, there are 100 natural numbers, the sum of which is 2010. It is known that the even number of these numbers is more than the odd number. Among these 100 numbers, there are at least 52 even numbers and at least 2 odd numbers