Backtracking - diceRoll, diceSum - https://www.youtube.com/watch?v=tC1rgphJtO4

dice.ts

/**
 * Prints all possible combinations of values that could appear after rolling the dice.
 */
function diceRoll(dice: number, chosen: number[]) {
  if (dice == 0) {
    // Base case, print.
    console.log(chosen);
  } else {
    for (let i = 1; i <= 6; i++) {
      // Chose
      chosen.push(i);
      // Explore
      diceRoll(dice - 1, chosen);
      // Un-choose
      chosen.pop();
    }
  }
}

/**
 * Prints all possible combinations of dice values that sum up to targetSum.
 */
function diceSum(dice: number, targetSum: number, sum: number, chosen: number[]) {
  if (dice == 0) {
    // Base case: if we eliminated unnecessary calls,
    // we should end up with chosen values that give us the desired sum by default.
    console.log(chosen);
  } else {
    for (let i = 1; i <= 6; i++) {
      // Explore only solution that might give us a sum <= targetSum:
      //  Given i, what's smallest and biggest possible values we can get
      //  by rolling the current die + all remaining dice?
      const smallestSum = sum + i + 1 * (dice - 1); // Get a 1 on all remaining dice.
      const biggestSum = sum + i + 6 * (dice - 1); // Get a 6 on all remaining dice.
      if (smallestSum <= targetSum && biggestSum >= targetSum) {
        chosen.push(i);
        diceSum(dice - 1, targetSum, sum + i, chosen);
        chosen.pop();
      }
    }
  }
}

diceRoll(2, [])
// [ 1, 1 ]
// [ 1, 2 ]
// [ 1, 3 ]
// [ 1, 4 ]
// [ 1, 5 ]
// [ 1, 6 ]
// [ 2, 1 ]
// [ 2, 2 ]
// [ 2, 3 ]
// [ 2, 4 ]
// [ 2, 5 ]
// [ 2, 6 ]
// [ 3, 1 ]
// [ 3, 2 ]
// [ 3, 3 ]
// [ 3, 4 ]
// [ 3, 5 ]
// [ 3, 6 ]
// [ 4, 1 ]
// [ 4, 2 ]
// [ 4, 3 ]
// [ 4, 4 ]
// [ 4, 5 ]
// [ 4, 6 ]
// [ 5, 1 ]
// [ 5, 2 ]
// [ 5, 3 ]
// [ 5, 4 ]
// [ 5, 5 ]
// [ 5, 6 ]
// [ 6, 1 ]
// [ 6, 2 ]
// [ 6, 3 ]
// [ 6, 4 ]
// [ 6, 5 ]
// [ 6, 6 ]

diceSum(2, 7, 0, []);
// [ 1, 6 ]
// [ 2, 5 ]
// [ 3, 4 ]
// [ 4, 3 ]
// [ 5, 2 ]
// [ 6, 1 ]