## Square any number in less than a second

### 26-09-2015 | Posted in Problem solving

This week’s interview of Arthur Benjamin in the Huffington Post gives an excellent illustration of quick problem solving.

In this video, he explains the trick to quickly square a number.

This problem-solving strategy is called *Analogy*.

## How does Analogy work?

When faced with a problem, try to find a similar problem that is simpler. Solve that. Now you’re left with the question of how to go from there to a solution for the original problem.

The example in the video is to square 498. A quick way to do that it to apply *Analogy* twice:

- Find a similar problem that is simpler: 500 × 496 (two up; two down).
- That’s still not obvious, but a simpler problem exists: 1000 × 496 = 496,000
- From that solution, you quickly find 500 × 496 = 248,000 (by dividing by two)
- We’re left with the question: how to move from that to 498
^{2}? Benjamin has that memorized: by adding the square of two: 498^{2}= 248,004

In case you were wondering, the reason for that is that x^{2}= (x – n) × (x + n) + n^{2}

So use the Analogy problem-solving strategy to make your problems simpler. It requires some creativity, but it can lead to extremely fast results!