HomeNon-Routine Mathematics

## Introduction to Non-Routine Mathematics / Non-Routine Problem Solving

Creative problem solving or Non-Routine Mathematics involves finding solutions for unseen problems or situations that are different from structured Maths problems. There are no set formulae or strategies to solve them , and it takes creativity, flexibility and originality to do so. This can be done by creating our own ways to assess the problem at hand and reach a solution. We need to find our own solutions and sometimes derive our own formulae too.

A non-routine problem can have multiple solutions at times, the way each one of us has different approach and different solutions for our real-life problems.

__Why non-routine Mathematics__

- It’s an engaging and interesting way to introduce problem solving to kids and grown-ups.
- Its helps boost the brain power.
- It encourages us to think beyond obvious and analyse a situation with more clarity.
- Encourages us to be more flexible and creative in our approach and to think and analyse from an extremely basic level, rather than just learning Mathematical formulae and trying to fit them in all situations.
- Brings out originality, independent thought process and analytical skills as one must investigate a problem, reach a solution, and explain it too.

**How to Analyse a Non-Routine Problem**:

- Read the problem well and make note of the
to you.*data given* - Figure out clearly
or what is expected from you.*what is asked* - Take note of all the
. This will help you get more clarity.*conditions and restrictions* up the problem*Break*, try to solve these smaller problems first.*into smaller parts*- Make a note of
or any*data and properties*( faced earlier)*similar situations* - Look for a
or think about a*pattern*of reaching a solution.*logical way*or*Make a model*.*devise a strategy* - Use this
to reach a solution.*strategy and your knowledge*

Let’s try a few examples!

**Example 1:**

There are 50 chairs and stools altogether in a restaurant. Find the number of chairs and the number of stools, if each chair has 4 legs and each stool has 3 legs and there are 180 wooden legs in the restaurant?

**Solution:**

First thing that comes to our mind is that we have two algebraic equations here and solving simultaneous equations is the only way to get a solution.

**Not really!** A small child and a Non-Math student can solve it too.

Logic: Each piece of furniture has at least 3 legs (stools-3 legs, chairs -4 legs).

So, minimum number of legs (for 50 pcs of furniture) in the restaurant = 3 X 50 = 150 legs *if there are only stools in the restaurant. *

Chairs have 4 legs i.e., each extra leg belongs to a chair.

(we have already taken 3 legs of each chair and stool into account)

Number of extra wooden legs in the restaurant

= total number – minimum possible number of legs for 50 pcs of furniture

= 180 -150 = 30 legs

Each extra leg (4^{th} leg) belongs to a chair.

Therefore, the number of chairs in the restaurant = 30

So, number of stools = 50-30=20

For more on this topic: Solving without Simultaneous Equations

__Example 2:__

A cube is painted from all sides. It is then cut into 27 equal small cubes. How many cubes

- Have 1 side painted?
- Have 3 sides painted?

__Solution: __

The cube is cut into 27 equal cubes of equal size that means it’s a 3x3x3 cube. Visualise the cube (have included 3x3x3 Rubix cube pic for reference)

a) Only the cubes at the centre of each face (that are located neither at corners nor along the edges) will have just one side painted.

In a 3 x 3 cube there is only one cube on each face which is located neither at corners nor along the edges.

There are 6 faces in any cube.

Therefore, ** 6 cubes** have only one side painted.

b)The small cubes at the corners of the big cube have 3 sides painted.

There are 8 small corner cubes in the big cube.

Therefore, ** 8 cubes** have 3 sides painted.