Lighter than the rest!

Logic Level 2

You have 16 eggs, one of them is lighter than the rest.

Using an equal arm balance, what is the minimum number of balancings you need to determine the light egg?

6 5 2 4 3

5 solutions

Mustafa Lokhandwala
May 9, 2014

First put 8 eggs on each scale. One scale will weigh less. Take 6 out of the 8 eggs form the lighter scale and put 3 of them on each scale. If the scale is balanced, the lighter egg is out of the remaining 2 eggs. If the scale is unbalanced, take two eggs out of 3 from the lighter scale and balance them. If balanced, the remaining egg is lighter. if unbalanced, the egg on the lighter scale is lighter than the rest. So,a total of 3 steps in each case.

This question is poorly worded, it does not state that the rest of the eggs weigh the same. So if the rest of the eggs are of random weights (but still heavier than the light egg) the answer is n-1 where n is the number of eggs (16) and we would need to do 15 balancings using binary search.

Gwion Davies - 5 years, 10 months ago

In another variant of this question, we know that one egg is either lighter or heavier than the rest. In that case, how can we solve the problem? NOTE- I don't know the answer. I will be grateful if someone could tell me.

Shabarish Ch - 7 years ago

I think the minimum number of balancings is 1. My reasoning is as follows. Pick two eggs at random and put one on each scale. If one of the eggs you chose happened to be the lighter one, then you already know the answer. Of course, the maximum number of tries for such a method would be far greater than the optimal solution of 3, but the minimum is lower.

Daniel Johnston - 5 years ago

Based on the question, the answer is 1. You put the lightest egg on one side and another on the other side and that will determine which is the lightest egg

Brandyn Pryce - 4 years, 10 months ago

You can use a similar method for 5 eggs first and the second set of 3 eggs

Kamala Ramakrishnan - 7 years ago

Nguyen Thanh Long
May 21, 2014

Divide eggs into four parts: two groups of 5 eggs and two groups of 3. Compare two groups of 5, (1) if balance compare two groups of 3, find one lighter group. In three eggs: compare two eggs find one lighter. (2) if not compare two groups of 2 eggs, if not balance: compare two eggs lighter, otherwise the lighter is found. So number of balances is: $\boxed{3}$

first put 8 eggs on either side.now check lighter side .take 8 eggs from lighter side and put 4-4 on both side .now again check lighter side.now take 4 eggs of lighter side and divide2-2 on either side.check lighter one.now divide 1-1either side.lighter one contains ligher egg

jack jain - 6 years, 11 months ago

the total no of attempts will be 4 in this case

Amit Yadav - 6 years, 10 months ago

Noor Abbas Qureshi
Dec 19, 2014

we can know it by dividing the total first into 8/8 then 4/4 and then 2/2 by balancing each time

Test Test
Jun 30, 2014

Solution : 3 Description : Divide eggs in groups of 6-6-2-2. Compare 6-6, if imbalanced take lighter 6 eggs divide in 3-3 and compare, take lighter and compare 1-1. If 6-6 are balanced then compare 2-2 and finally 1-1.

Esha Raghute
Dec 31, 2014

What to do if the problem includes big numbers like 132 sacks and one out of 132 is the lighter one...how to decide the grouping and what will be the solution then??

Since you can do groups of 3 it would be log base 3 of 132 and round up. So 3, 9, 27, 81, 243... In this case, anything 27 or less can be done in 3.

Cory Cameron - 6 years, 2 months ago

Lighter than the rest!

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