Question20. How many different representations of -3 can be made with 20 or fewer counters?

Studdy Solution
Determine the range of $p$ and $n$:
Since $n = p - 3$, and both $n$ and $p$ must be non-negative integers, we have:
$$p \geq 3$$
Thus, the range for $p$ is $3 \leq p \leq 11$.
For each $p$ in this range, calculate $n = p - 3$.
Count the number of valid $(p, n)$ pairs:
$$p = 3, 4, 5, \ldots, 11$$
This gives us 9 possible values for $p$.
The number of different representations of $-3$ with 20 or fewer counters is:
$\boxed{9}$