10 Coins Puzzle - 10 Coins Blindfolded Puzzle - Interview Puzzles

Puzzle Details: 

You are blindfolded and 10 coins are placed in front of you on the table. You are allowed to touch the coins but can’t tell which way up they are by feel. You are told that there are 5 coins heads up, and 5 coins tails up but not which ones are which. How do you make two groups of coins each with the same number of heads up? You can flip the coins any number of times.

This puzzle was asked in many companies and other interviews since these kinds of puzzles help to find the logical thinking ability of the candidates.

Solution:

initially, this puzzle looks like a complicated one, but this is a simple puzzle if you know the logic. here is the correct way to approach it...

the logic is ==> Make 2 groups with an equal number of coins. Now, flip all the coins in one of the groups.

This will do the magic, let's check, How this will work with a couple of examples? .... let's take an example, So initially there are 5 heads and 5 tails, suppose if you divide it into 2 groups there are multiple possibilities. let us consider 2 possibilities, where the logic holds valid.

In Case 1:
assume that group P1 has coins with 2 heads and 3 tails: H H T T T
group P2 has coins with 3 heads and 2 tails: H H H T T
Now P1 will be flipped, after flipping, P1 has 2 tails and 3 heads: T T H H H
Now we can clearly see that number of heads in a group1 is equal to the number of heads in group2.
In this example, I have selected a group1 to flip, but you can choose any group to flip still we can achieve the result.
P1(Heads) = P2(Heads)

In Case 2:

In this case assume that group P1 has coins with 1 head and 4 tails: H T T T T
group P2 has coins with 4 heads and 1 tail: H H H H T
Now when P1 is flipped, we can see that number of heads in group1 is equal to the number of heads in group2.
P1: H H H H T
P1(Heads) = P2(Heads)

In this way we can make sure that the number of heads is equal in both groups logically, using these simple steps.

Note: there is only one case that will not guarantee that number of heads is equal in both groups, that is when the number of heads in any of the groups is 5, and if you choose the same group to flip. In this scenario, all coins in both groups have tails up which is not the expected output. I would suggest you remember this scenario.