# How many kids-Math riddle

Parties are a time for joy and celebration, especially when kids are involved. But what's even more exciting is when we can use math to solve a puzzle related to a party! In this blog post, we'll tackle a delightful challenge involving juice, cake, and some clever counting. Join us as we discover the total number of kids at the party.

At a children's party,
10 kids had juice,
8 kids had cake,
and 6 kids had juice and cake.
How many kids were there at the party?

Explanation :

We have the following information:

10 kids had juice (J).
8 kids had cake (C).
6 kids had both juice and cake (J ∩ C).
To find out how many kids were at the party in total, we can use set theory and the principle of inclusion-exclusion:

Total kids = (Kids with juice) + (Kids with cake) - (Kids with both juice and cake)

Total kids = 10 (J) + 8 (C) - 6 (J ∩ C)

Now, let's adjust the equation based on the information you provided:

Since 6 kids had both juice and cake, there are 8 - 6 = 2 kids who had cake (C) but not juice.

So, the adjusted equation becomes:

Total kids = 10 (J) + 2 (C, without J) - 6 (J ∩ C)

Now, plug in the values:

Total kids = 10 + 2 - 6
Total kids = 12

Therefore, there were 12 kids in total at the party. This method uses set theory and the principle of inclusion-exclusion to find the total number of kids, considering both the ones with juice and cake and those with only cake.

Through a bit of math and the Inclusion-Exclusion Principle, we've solved the puzzle and found that there were 12 kids at the party. It's a wonderful example of how math can be applied to everyday situations, even the most fun-filled ones like children's parties. Keep exploring the magic of numbers and enjoy your next party with a bit of math puzzling!