Three Squares | Puzzles for Interview - Interview Preparation PDF Download

Problem Statement

You are provided with four sticks of length 'a' and four more sticks of length 'b'. The length of 'b' is exactly half of the length of 'a'. Your task is to create three equal squares using all the given 8 sticks.

Solution

To solve this problem, we need to figure out how to use the available sticks to form three squares of equal size. Since we have four sticks of length 'a' and four sticks of length 'b', let's see if there's a way to use these sticks to form the sides of the squares.

First, let's use two sticks of length 'a' to form one side of a square. Since the length of 'b' is half of the length of 'a', we can take two sticks of length 'b' and place them end-to-end to create a length equal to 'a'. So, now we have three sides of the square with length 'a'.

Now, for the last side of the square, we can use the remaining two sticks of length 'b' and place them end-to-end, again creating a length equal to 'a'. This completes one square of side 'a'. We have used all four sticks of length 'b' to form this square.

Next, we can use the remaining two sticks of length 'a' to form the sides of two smaller squares. Since the length of 'a' is double the length of 'b', we can cut each stick of length 'a' in half to obtain four sticks of length 'b'. This will give us four sticks of length 'b' to form the sides of the two remaining squares, with each square having sides of length 'b'.

In summary, we can create three equal squares by forming one square with sides of length 'a' using two sticks of length 'a' and four sticks of length 'b', and forming two smaller squares with sides of length 'b' using the remaining two sticks of length 'a' cut in half.

Conclusion

The given puzzle of creating three equal squares with four sticks of length 'a' and four sticks of length 'b' can be solved by strategically using the sticks to form the sides of the squares. By forming one square with sides of length 'a' using two sticks of length 'a' and four sticks of length 'b', and creating two smaller squares with sides of length 'b' using the remaining two sticks of length 'a' cut in half, we can successfully create three equal squares using all given sticks.