Marbles Puzzle

There are 100 jars each with infinite marbles. All are 10 grams except one jar which has all 9-gram marbles.
How would you find which jar by weighing only once?

Solution

Consider you have 5 jars and look at the solution below.
To find the contaminated Jar, follow this approach :

Step 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.
Step 2: Put all these 15 marbles on the scale. The correct weight is 15*10 =150.

But one of the jars has contaminated marble. So the weight will definitely be less than 150.

Step 3: If the weight is 149 then jar 1 has contaminated marble because there is only one contaminated marble. If the weight is 148 then jar 2, if the weight is 147 then jar 3, if 146 then jar 4, if 145 then jar 5.
Your task is to relate as per 100 jars. 😛