Biggest coin first

With Indian coins of 20, 10, 5, 2 and 1, always take as many of the biggest coin as fit, then move to the next. These coins are designed so that biggest-first always gives the fewest coins.

Dividing rather than subtracting one coin at a time means even a billion rupees takes only five steps.

Largest to smallest: go through the coins in that order.

Divide, don't subtract: one division handles any amount in five steps.

In code

count = 0
for d in (20, 10, 5, 2, 1):
    count += amount // d
    amount %= d
return count

Owe ₹67 · coins, biggest first

coin

owed: 7
coins: 3

₹20: 67 divided by 20, rounded down, is 3, so 3 coins fit. That covers 60, so ₹7 is still owed.

Move 1 of 5

Greedy isn't always right

With made-up coins of 1, 3 and 4, and an amount of 6, biggest-first takes 4 + 1 + 1, which is 3 coins. But 3 + 3 uses only 2.

Greedy is safe here only because real coin systems are designed so that it works. Later, dynamic programming handles any coin set.

Check before trusting greedy: ask whether a big choice now could block a better finish.