Turn a tangle of IOUs into two payments

The end-of-trip tangle

Six friends, five days, dozens of shared costs. By the end, Ravi owes Priya, Priya owes Sam, Sam owes Ravi, and everyone owes the person who booked the hotel. If each pair settles directly, that's potentially fifteen separate transfers for a group of six. Nobody does that; instead the debts quietly get forgotten.

Debt simplification exists to collapse that web into the fewest possible payments — often just two or three for the whole group.

How simplification works, plainly

It ignores who-paid-for-what-specifically and looks only at each person's net position: how much they're up or down overall. Then it matches the people who are owed against the people who owe, so money flows in as few hops as possible.

• --Everyone's individual charges are netted into a single balance (+ or −).
• --The biggest debtor pays the biggest creditor first, and so on down the line.
• --The result settles the exact same amounts — just with far fewer transactions.

Why fewer payments actually matters

It's not just tidiness. Fewer transfers mean fewer chances for someone to forget, fewer “did you send it?” follow-ups, and no awkward tiny ₹40 transfers between people who also owe each other ₹38 the other way. The group closes the books in one round and moves on.