I came across this rather beautiful example on the importance of perception the other day. How when viewed differently seemingly difficult problems can become child’s play.
Consider for example this question:
Two players are playing a game and take alternating turns. Initially, there are 9 cards with numbers from 1 to 9 on the table. On each turn, a player takes one of the cards. The first player to have exactly 3 cards with numbers that sum to 15 wins. If no one can after all cards are distributed, then it’s a draw.
1 2 3 4 5 6 7 8 9
Developing an algorithm for solving this problem can get fairly tricky.Just give it some thought and think of how you would play the game.
No seriously stop. Give it some thought.
Okay now here’s what American polymath Herb Simon did. He devised a beautiful way of solving this problem by merely changing the orientation of the cards in the form of a 3*3 matrix
2 7 6
9 5 1
4 3 8
Now all you have to do is play X and 0. 😀