Final answer:
The given equation n = 3f + 3 describes a linear relationship between the number of counters and the figure number. Solving the equation for a figure with exactly 100 counters, we find that it does not satisfy the relationship.
Step-by-step explanation:
The given relationship between n and f is n = 3f + 3. This equation describes a linear relationship between the number of counters (n) and the figure number (f). We can rearrange the equation to find the value of f for a given n. The equation becomes f = (n - 3) / 3. This can also be understood from the equation itself, as 100 is not a multiple of 3.
To have a figure with exactly 100 counters, we need to find the corresponding value of f using the equation. Plugging in n = 100, we get f = (100 - 3) / 3 = 97 / 3. Since f is the figure number, it should be a whole number. However, 97/3 is not a whole number, which means there is no figure with exactly 100 counters that satisfies this relationship.
This result may also be evident from the equation itself. Since the coefficient of f is 3, any value of f will result in a multiple of 3 for n. Since 100 is not a multiple of 3, it cannot be the value of n for any figure in this relationship.