# Heuristics, Problem Solving and Fake Coin

Two main problem solving techniques are algorithms and heuristics. While algorithms involve detailed, step wise process to solve a problem, heuristics is about short cuts and rule of thumb. There are advantages of using heuristics, esp.as it is time saving and you can use your existing knowledge to solve familiar problem.

Heuristics has one major drawback – mental set- which is the tendency of people to only use solutions that have worked in the past rather than looking for alternative ideas. You are comfortable with your existing knowledge as it serves purpose; coming out of comfort zone is not something you are eager to do.

In psychology, problem of identifying a fake coin is used to identify this kind of mindset.

The problem consists of 8 coins, of which one is fake, and fake coin is lighter than genuine coin by 1 gram. You have to identify fake coin using a weighing scale in two trials i.e. number of times you can use scale is two. Heuristics will force us to use two stacks of 4 coins each, find out the which stack is lighter, then go for lighter stack, and split them into stack of two coins each and find out which stack is lighter, you can solve problem in third trail. Whatever combination you use, stack of 4 coins is never going to solve the problem in two trials.

Here you have to be creative and think different, instead of usual combination of two stacks of 4, go for 3 stacks of coins – 2 stacks of 3 coins each and one of two coins. Let us label them ABC, EFG, HI. First balance two 3 stacks of coins i.e. ABC and EFC. Solution is as follows.

If ABC < EFG, then fake coin is either A or B or C. Of three pick any two coins, say A & B and weigh them. If A = B, then C is fake, if A < B, then A is fake.

Now other option could be ABC= EFG, then either H or I is fake, so in second trial use H and I, you can detect fake.