Induction is the creative part of science. The scientist must carefully study a phenomenon, then formulate a hypothesis to explain the phenomenon. Scientists who get the most spectacular research results are those who are creative enough to think of the right research questions.
Natural sciences (physics, chemistry, biology, etc.) are inductive. Evidence is collected. The Scientific Method is applied. Start with specific results and try to guess the general rules. Hypotheses can only be disproved, never proved. If a hypothesis withstands repeated trials by many independent researchers, then confidence grows in the hypothesis. All hypotheses are tentative; any one could be overturned tomorrow, but very strong evidence is required to overthrow a "Law" or "Fact".
Specific -> General
Here's an example of induction: Suppose I have taken 20 marbles at random from a large bag of marbles. Every one of them turned out to be white. That's my observation - every marble I took out was white. I could therefore form the hypothesis that this would be explained if all the marbles in the bag were white. Further sampling would be required to test the hypothesis. It might be that there are some varicolored marbles in the bag and my first sample simply didn't hit any.
Incidentally, this is one case where we could prove the hypothesis true. We could simply dump out all the marbles in the bag and examine each one.
Mathematics is a deductive science. Axioms are proposed. They are not tested; they are assumed to be true. Theorems are deduced from the axioms. Given the axioms and the rules of logic, a machine could produce theorems.
General -> Specific
Start with the general rule and deduce specific results. If the set of axioms produces a theorem and its negation, the set of axioms is called INCONSISTENT.
By the way, when Sherlock Holmes says that he uses "deduction," he really means "induction." Of course, one can fault his creator, Sir Arthur Conan Doyle, who believed in spirit mediums and faeries.
Suppose we have the following known conditions.
How about this?