Heaviest Coin Bag Algorithm | Dataford Interview Questions

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Problem

During an NVIDIA H100 validation run, a calibration fixture contains 10 labeled bags, each holding 10 coins. Nine bags contain coins weighing normal_weight grams, while every coin in exactly one bag weighs heavy_weight grams. The heavier bag must be identified with one weighing.

Before weighing, remove 1 coin from bag 1, 2 coins from bag 2, and so on through 10 coins from bag 10. Weigh all 55 selected coins together. Implement a function that returns the 1-based label of the bag containing the heavier coins.

Formal Specification

Implement find_heavy_bag(measured_weight, normal_weight, heavy_weight).

measured_weight, normal_weight, and heavy_weight are positive integers representing grams.
The function returns an integer from 1 through 10.
Assume heavy_weight > normal_weight and exactly one bag is heavy.

Constraints

There are exactly 10 bags.
Each bag contains exactly 10 coins.
1 <= normal_weight < heavy_weight <= 1000.
The measured weight exactly matches one valid heavy-bag configuration.
The returned bag label must be an integer from 1 through 10.

Function Signature

def find_heavy_bag(measured_weight, normal_weight, heavy_weight):