You are given 8 pennies, 7 of which weigh exactly the same, but one penny weighs less than the other 7. You also have a judge scale. Find the one penny that weighs the least in less than 3 steps.
Like most puzzles, the answer to this question is not going to just jump out to you – you’ll have to break the question down.
We know that a judge scale is used to compare the weights of different things and it tells us if something on one side is heavier, lighter, or the same weight as whatever is on the other side of the scale.
Since the question asks us to find the penny that weighs the least in less than 3 steps, that means that we will need to find the lightest penny in either 1 or 2 steps.
So, let’s think of finding the answer to this in 1 step: Really, the only thing we can do is compare 2 pennies on the scale and if one is lighter than the other than we know that it is the lightest. But, we would have to be lucky enough to pick the lightest penny to compare, and there’s no way we can do this without just getting plain lucky. So, there’s also no way we can do this in 1 step.
Has to be done in 2 steps
Now, we have to be able to do this in 2 steps – so how is this possible? What if we just tried dividing the 8 pennies into groups? Let’s create 2 groups of 3 pennies each, and 1 group of 2 pennies.
Now, let’s put the 2 groups of 3 pennies on the scale. What do we know if they are equal? Well, if they’re equal then the lightest penny must be in the group of 2!
Then, let’s take 2 pennies in the group of 2 and compare them to each other. They can’t possibly be equal, so we know that the lighter one is our lightest penny! Bravo – we have an answer in 2 steps.
But, what if when comparing the 2 groups of 3 pennies, it didn’t turn out that they were equal? Well, one of the groups of 3 would be lighter, which means that the lighter penny would be in that group.
So, we could take 2 pennies out of that group of 3 and compare them. If they’re equal we know the 3rd penny is the lightest. If one is lighter than the other, then we know that penny is the lightest. So, again the problem is solved in 2 steps.
Summary of the solution
Here’s a summary of the solution: