Maximum Chocolate

The Puzzle: You have $15.

• Each chocolate costs $1.
• You can exchange 3 wrappers for 1 new chocolate. What is the maximum number of chocolates you can eat?

1. The Breakdown

1. Initial Purchase: $15 gives you 15 chocolates. (Wrappers = 15).
2. First Exchange: Exchange 15 wrappers for 5 new chocolates. (Wrappers = 5).
3. Second Exchange: Exchange 3 out of your 5 wrappers for 1 new chocolate.
   • (Wrappers remaining: 2 from before + 1 brand new = 3 wrappers).
4. Third Exchange: Exchange those 3 wrappers for 1 final chocolate. (Wrappers = 1).

2. The Total

Summing them up: $15 + 5 + 1 + 1 = \mathbf\{22\}$ chocolates.

Interview-Focused Questions

function countMax(money, price, wrap) {
  let count = Math.floor(money / price);
  return count + countMore(count, wrap);
}
function countMore(wrappers, wrap) {
  if (wrappers < wrap) return 0;
  let newChoc = Math.floor(wrappers / wrap);
  let extra = wrappers % wrap;
  return newChoc + countMore(newChoc + extra, wrap);
}

Key Takeaway

This is a test of Iterative Thinking. Most people miss the fact that the “new” chocolates also come with wrappers that can be reused.