Case 1: When America began the launch of astronauts into space, they found out that the pens wouldn't work at zero gravity (Ink won't flow down to the writing surface). To solve this problem, it took them one decade and $12 million. They developed a pen that worked at zero gravity, upside down, underwater, in practically any surface including crystal and in a temperature range from below freezing to over 300 degrees C. And what did the Russians do? They used a pencil.
Case 2: One of the most memorable case studies on Japanese management was the case of the empty soapbox, which happened in one of Japan's biggest cosmetics companies. The company received a complaint that a consumer had bought a soapbox that was empty. Immediately the authorities isolated the problem to the assembly line, which transported all the packaged boxes of soap to the delivery department. For some reason, one soapbox went through the assembly line empty. Management asked its engineers to solve the problem.
Post-haste, the engineers worked hard to devise an X-ray machine with high-resolution monitors manned by two people to watch all the soapboxes that passed through the line to make sure they were not empty. No doubt, they worked hard and they worked fast but they spent a whoopee amount to do so.
But when a file employee in India in a small company was posed with the same problem, he did not get into complications of X-rays, etc., but instead came out with another solution. He bought a strong industrial electric fan and pointed it at the assembly line. He switched the fan on and as each soapbox passed the fan, it simply blew the empty boxes out of the line.
Moral of the story: Always look for simple solutions.
Devise the simplest possible solution that solves the problems. Always focus on solutions and not on problems. So at the end of the day, the thing that really matters is how one look into the problem, mere perceptions can solve the toughest of problems. You can start today.