Suppose you have 100 coins. 96 of them are heavy and 4 of them are light. Nothing is known regarding

Annika Miranda

Annika Miranda

Answered question

2022-06-02

Suppose you have 100 coins. 96 of them are heavy and 4 of them are light. Nothing is known regarding the proportion of their weights. You want to find at least one genuine (heavy) coin. You are allowed to use a weight balance twice. How do you find it?
Assumptions:
Heavy coins all have the same weight; same for the light coins.
The weight balance compares the weight of two sides on the balance instead of giving numerical measurement of weights.

Answer & Explanation

Sarahi Rollins

Sarahi Rollins

Beginner2022-06-03Added 2 answers

Divide the coins into three groups: A with 33 coins, B with 33 coins and C with 34 coins.
Weigh A and B against each other.
Now if A is heavier than B, then A cannot have two or more light coins, as in that case, A would be lighter (or equal to B). Now split A into groups of 16 plus one odd coin. Weigh the groups of 16 against each other. If they are the same, then any of those coins is heavy. If not, then any of the heavier 16 coins is heavy.
Consider the case when A and B are equal.
The possibilities for A, B and C are:
A B C 33 H 33 H 30 H + 4 L 32 H + L 32 H + L 32 H + 2 L 31 H + 2 L 31 H + 2 L 34 H
Now move one coin from A to B (call the resulting set B ) and weigh it against C.
If B > C, then the coin you moved from A is a heavy coin.
If B = C, then the coin you moved from A is a light coin and the remaining coins in A are heavy.
If B < C, then all the coins in C are heavy.

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