A) The collection of positive integers whose sum is 100 are: 23, 17, 6, 54, 0.
B) Another collection of positive integers whose sum is 100 are: 13, 27, 4, 56, 0.
C) Due to the fact that the units can be commuted, their sum is always equal to 20.
D) The smallest possible value is 0 and the largest is 57.
A) The formation of a collection of positive integers can be done by trial and error. For example, only using the digits {0, 1, 2, 3, 4, 5, 6, 7}.
For example, we can have;
23 + 17 + 6 + 54 + 0 = 100
Where the numbers used are: 23, 17, 6, 54, 0.
B) Another example is;
13 + 27 + 4 + 56 + 0 = 100
C) If we add the units digits of these 5 numbers, we get:
3 + 7 + 6 + 4 + 0 = 20
Now, if we compute the units digits between the different numbers, to get for example: 27, 13, 6, 54, 0
The sum is still equal to 100, and the units digits are the same ones, so we still have that the sum of the units digits is equal to 20.
d) The smallest integer that we use is 0.
For the largest we just commute the tens and units digits so we make the larger integer possible, which is:57.
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