Computability

Computability is like a game of puzzles where a computer tries to solve a problem. Imagine you have a box full of toys, and you need to find a specific toy inside. You can look through each toy until you find the one you want, but that takes a lot of time and effort. However, if your parent has given you a special toy-locator device, you can use it to find the toy quickly.

In the same way, computers can solve problems by following a set of instructions given by a programmer. These instructions are like a toy-locator device that tells the computer exactly what to do to solve a problem. But not all problems can be solved by computers – some problems are just too hard!

Just like how some puzzles for adults are too difficult for children, some problems are too difficult for computers to solve. These problems are called "unsolvable" or "undecidable" problems. In other words, there is no set of instructions the computer can follow to solve them.

However, some problems can be solved by computers using a special type of program called an algorithm. Think of an algorithm as a set of step-by-step instructions, like a recipe for baking a cake. The computer follows each step of the algorithm, just like you would follow each step in the recipe. If the algorithm is good, the computer will eventually find the solution to the problem.

In summary, computability is the study of what problems can and cannot be solved by computers. Just like how some puzzles are too hard for children, some problems are too hard for computers. But with the right instructions, computers can solve many problems through algorithms.