What is the minimum number of colour pencils required to fill the spaces in the below figure with no two adjacent spaces have the same colour? <img src="/api/images/minimum-colours-triangle-puzzle.png" alt="Puzzle image showing a complex triangle divided into multiple adjacent regions, asking for the minimum number of colour pencils needed so that no two adjacent regions share the same colour" width="300" height="200" loading="lazy" decoding="async" class="rounded border border-gray-300 mx-auto my-4" />

Question: What is the minimum number of colour pencils required to fill the spaces in the figure such that no two adjacent spaces have the same colour?

Step 1: Understand the problem

This is a classic graph colouring problem where each distinct region in a geometric figure must be coloured such that no two touching (adjacent) regions share the same colour.

Step 2: Analyze the figure

The figure appears to be a triangle divided into smaller regions — some triangular, some trapezoidal — all connected in a way that many regions share borders.

Step 3: Apply graph colouring logic

• The goal is to assign colours to the regions such that adjacent regions do not have the same colour.
• This is similar to colouring a map — adjacent "countries" need different colours.
• By carefully examining the layout and using a greedy colouring approach, we can determine the chromatic number (minimum number of colours required).

Step 4: Result

With smart arrangement and using non-touching colouring strategy, the puzzle can be solved using only:

3 colour pencils

Note: Although the figure looks complex, a well-structured colouring pattern ensures that no more than 3 colours are necessary to fill all adjacent areas without conflicts.