Answer: No.
Explanation:
We have 10 lumps of sugar, and we want to divide them into 3 cups, in such a way that there is an odd number of lumps in each cup.
This only can happen if we have 3 odd numbers such that the addition is equal to 10.
Now 10 is an even number, remember that even numbers can be written as:
2*k
where k is an integer number.
And odd numbers can be written as:
2*n + 1
where n is an integer.
Then we have 3 odd numbers, let's call them:
(2*n + 1), (2*k + 1) and (2*p + 1).
Now let's add them:
(2*n + 1) + (2*k + 1) + (2*p + 1).
2*(n + k + p) + 1 + 1+ 1
2*(n + k + p) + 2 + 1 =
2*(n + k + p + 1) + 1.
Now, the number n + k + p + 1 is an integer number, let's call it X, then we have that the addition of the 3 odd numbers is:
2*X + 1
This is an odd number
So for any 3 odd numbers that we add together, the result will always be an odd number.
Then is impossible to add 3 odd numbers and get 10 as the result (Again, 10 is an even number).
Then is not possible to have an odd number of lumps in each cup.