The most straightforward solution uses multiple nested loops to generate all possible combinations: ```

const possibleAverages = new Set(); for (let r1 = 1; r1 <= 5; r1++) { for (let r2 = 1; r2 <= 5; r2++) { for (let r3 = 1; r3 <= 5; r3++) { for (let r4 = 1; r4 <= 5; r4++) { for (let r5 = 1; r5 <= 5; r5++) { for (let r6 = 1; r6 <= 5; r6++) { const avg = (r1 + r2 + r3 + r4 + r5 + r6) / 6; possibleAverages.add(avg); } } } } } } console.log(possibleAverages.size);

While this works, it's inefficient and doesn't scale well with more raters. ### Recursive Solution

A more elegant approach uses recursion to handle any number of raters: ```

const uniqueAverages = new Set();
function calculateAverages(ratersRemaining, currentTotal = 0) {
  if (ratersRemaining === 0) {
    uniqueAverages.add(currentTotal / 6);
    return;
  }
  for (let score = 1; score <= 5; score++) {
    calculateAverages(ratersRemaining - 1, currentTotal + score);
  }
}
calculateAverages(6);
console.log(uniqueAverages.size);

This solution is more flexible but still computes all possible combinations. ### Mathematical Approach

The optimal solution recognizes that: - Minimum possible total score: 6 (all raters give 1)

• Maximum possible total score: 30 (all raters give 5)
• Each total between 6 and 30 is possible

Therefore, there are exact 25 possible distinct total scores (30 - 6 + 1), and consequently 25 possible distinct average scores.