Working backward to solve problems

We've talked a lot about inversion — solving problems backwards.

“To look ahead, it pays to look backwards.”

In this short video, grandmaster Maurice Ashley walks us through retrograde analysis, which is a method to solve game positions in chess by working backwards from known outcomes.

Take a look at this sentence.

After reading this sentence, you will realize that the the brain doesn't recognize a second ‘the.'

The second time around you realize you missed the second the the first time. But if you read the sentence backwards, you'd catch it.

The doubling bacteria problem.

Bacteria that double every 24 hours fill a lake it has infested after precisely 60 days. On what day was the lake half-full.

This problem is easiest solved backwards.

Finally, Ashley uses a card game. There are six cards in this game numbered 1 through 6. Whomever has the highest card wins. You pick a card and it says the number 2. I pick a card and offer a trade. Most people look at their card and say, 2 sucks. Looking only at this problem statistically, you're best to trade your card. However, assuming no trickery on my part, that may not the right move. To solve the problem, invert. If I had a 6 would I trade? No. What about the number 5? … Odds are I have a pretty crappy number if I want to trade.