With Indian rupees, the rule for the fewest notes and coins is simple: always take the biggest one that still fits, then repeat.
Say the change is ₹87. The biggest note that fits is ₹50, leaving ₹37. Then ₹20, leaving ₹17. Then ₹10, ₹5 and ₹2. That's ₹50₹20₹10₹5₹2: 5 pieces, and no other way does it in fewer.
This works because of how rupee notes and coins are spaced: 1, 2, 5, then 10, 20, 50, then 100, 200, 500. With that pattern, skipping the biggest piece never saves you anything. Some coin systems in history broke this rule, but the rupee doesn't.
A faster way in your head: break the amount into hundreds, tens and ones, and use the patterns below. ₹87 is ₹80 and ₹7, so ₹50₹20₹10 and ₹5₹2.
| Amount | Fewest pieces | Count |
|---|---|---|
| ₹1 | ₹1 | 1 |
| ₹2 | ₹2 | 1 |
| ₹3 | ₹2₹1 | 2 |
| ₹4 | ₹2₹2 | 2 |
| ₹5 | ₹5 | 1 |
| ₹6 | ₹5₹1 | 2 |
| ₹7 | ₹5₹2 | 2 |
| ₹8 | ₹5₹2₹1 | 3 |
| ₹9 | ₹5₹2₹2 | 3 |
| Amount | Fewest notes | Count |
|---|---|---|
| ₹10 | ₹10 | 1 |
| ₹20 | ₹20 | 1 |
| ₹30 | ₹20₹10 | 2 |
| ₹40 | ₹20₹20 | 2 |
| ₹50 | ₹50 | 1 |
| ₹60 | ₹50₹10 | 2 |
| ₹70 | ₹50₹20 | 2 |
| ₹80 | ₹50₹20₹10 | 3 |
| ₹90 | ₹50₹20₹20 | 3 |
| Amount | Fewest notes | Count |
|---|---|---|
| ₹100 | ₹100 | 1 |
| ₹200 | ₹200 | 1 |
| ₹300 | ₹200₹100 | 2 |
| ₹400 | ₹200₹200 | 2 |
The tens and ones patterns are the same shape: 1, 2, 5 and the 4 = 2 + 2 and 9 = 5 + 2 + 2 tricks. Learn one and you know the other.
| Customer | Change | Fewest pieces |
|---|---|---|
| Kulfi ×2, ₹80 paid ₹100 | ₹20 | ₹20 |
| Geometry box, ₹102 paid ₹200 | ₹98 | ₹50₹20₹20₹5₹2₹1 |
| Atta, 10 kg, ₹403 paid ₹500 | ₹97 | ₹50₹20₹20₹5₹2 |
| Mobile recharge, ₹259 paid ₹500 | ₹241 | ₹200₹20₹20₹1 |
| Milk, 1 litre, ₹66 paid ₹100 | ₹34 | ₹20₹10₹2₹2 |
Take the biggest note or coin that fits, subtract it, and repeat. With Indian rupees this always gives the fewest pieces.
6 pieces: ₹50 + ₹20 + ₹20 + ₹5 + ₹2 + ₹2.
Three coins: ₹5 + ₹2 + ₹2.