Marble & Jar Puzzle

March 3, 2023

Jar that is filled with Light -Weighed Marbles: Marble and Jar

This is a marble and jar puzzle where you have jars filled with an infinite number of marbles. Your premise is the rule for finding the light-weighted marble jar. 

Premise – This is a marble and jar puzzle, where 100 jars are filled with infinite marbles. All the jars contain marbles that are 10 grams except one jar that is filled with only 9-gram marbles.

Rules – You have to weigh it only once.

Objective – Find the Jar with light-weighted marbles

Finding the light-Weighed Marble Jar

   Solution for Finding the light-Weighed Marble Jar

Let us firstly consider 5 jars and look at the similar problem with the 5 jars. Therefore, the approach to finding the light-weighted jar is as follows:-

  1. Take out 1 marble from jar 1, 2 marble from jar 2, 3 marble from jar 3, 4 marble from jar 4, and 5 marble from jar 5.
  2. Put these 15 marbles on the weighing scale.
  3. The correct weight would be 15\times 10 = 150

But, as we know that one of the jars is filled with less-weight marbles, so the weight on the scale will be less than 150.

Finding the light-Weighed Marble Jar

After doing the above steps let us now consider the reading on the weighing scale.

  • If the weight is 149 then the marble belongs to jar 1 because there is only one contaminated marble.
  • Similarly, if the weight is 148 then jar 2 because there are two contaminated marble.
  • If the weight is 147 then jar 3 because there are three contaminated marble.
  • If the weight is 146 then jar 4 because there are four contaminated marble.
  • If the weight is 145 then jar 5 because there are two contaminated marble.
Finding the light-Weighed Marble Jar

Therefore, your task is similar and related to 100 jars.

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   Solution for Finding the light-Weighed Marble Jar

Let us firstly consider 5 jars and look at the similar problem with the 5 jars. Therefore, the approach to finding the light-weighted jar is as follows:-

  1. Take out 1 marble from jar 1, 2 marble from jar 2, 3 marble from jar 3, 4 marble from jar 4, and 5 marble from jar 5.
  2. Put these 15 marbles on the weighing scale.
  3. The correct weight would be 15\times 10 = 150

But, as we know that one of the jars is filled with less-weight marbles, so the weight on the scale will be less than 150.

Finding the light-Weighed Marble Jar

After doing the above steps let us now consider the reading on the weighing scale.

  • If the weight is 149 then the marble belongs to jar 1 because there is only one contaminated marble.
  • Similarly, if the weight is 148 then jar 2 because there are two contaminated marble.
  • If the weight is 147 then jar 3 because there are three contaminated marble.
  • If the weight is 146 then jar 4 because there are four contaminated marble.
  • If the weight is 145 then jar 5 because there are two contaminated marble.
Finding the light-Weighed Marble Jar

Therefore, your task is similar and related to 100 jars.