色觉障碍（色盲）是指辨别颜色差异的能力降低。色觉正常的人能够将 6 种颜色（红、橙、黄、绿、蓝、紫）看作 6 个色带。 患有色觉障碍的 Deutan 无法区分以下两对颜色： (I) 红色和绿色， (II) 蓝色和紫色。 对于特定深浅的这 6 种颜色（红、橙、黄、绿、蓝、紫），当上述两对颜色相邻放置时，在 Deutan 看来它们就像是单个色带。他看到这 6 种颜色的一些示例如下。

1. Deduce the condition required to form exactly 4 bands of colour.

Normally, 6 colours placed in a line form 6 bands. For them to appear as 4 bands, there must be a reduction of 2 bands.
Since only adjacent pairs of (Red, Green) and (Blue, Violet) can merge into a single band, both pairs must be placed next to each other.

2. Calculate the number of ways to arrange the colours using the block method.

Treat the (Red, Green) pair as $1$ unit and the (Blue, Violet) pair as $1$ unit.
Including Orange and Yellow, there are $4$ units in total to arrange in a line, giving $4!$ ways.
Within their respective units, Red and Green can swap places ($2!$ ways), and Blue and Violet can swap places ($2!$ ways).
$\text{Total number of ways} = 4! \times 2! \times 2! = 24 \times 2 \times 2 = 96$

1. Find the number of arrangements where one specific pair (e.g., Red and Green) is adjacent.

Treat Red (R) and Green (G) as a single grouped unit. Together with the other 4 colours, there are 5 units to arrange.
Number of ways R and G are adjacent = $5! \times 2! = 120 \times 2 = 240$.

2. Find the number of arrangements where both problem pairs are adjacent (which results in 4 bands).

Treat R and G as one unit, and Blue (B) and Violet (V) as a second unit. Together with the 2 remaining colours, there are 4 units to arrange.
Number of ways both pairs are adjacent = $4! \times 2! \times 2! = 24 \times 2 \times 2 = 96$.

3. Calculate the number of arrangements where exactly one pair is adjacent, yielding exactly 5 bands.

To get exactly 5 bands, either ONLY R and G are adjacent, or ONLY B and V are adjacent.
Number of ways R and G are adjacent but B and V are not = $240 - 96 = 144$.
By symmetry, the number of ways B and V are adjacent but R and G are not is also $144$.
Total arrangements for exactly 5 bands = $144 + 144 = 288$.

1. Calculate the total unrestricted number of arrangements for the 6 colours.

$\text{Total unrestricted arrangements} = 6! = 720$

2. Calculate the number of arrangements where the indistinguishable pairs are adjacent.

For Deutan to see exactly 6 bands, Red & Green must not be adjacent, and Blue & Violet must not be adjacent.

Let's find the restricted arrangements:

• Number of arrangements where Red & Green are adjacent:
  Treat (Red, Green) as 1 unit $\Rightarrow 5! \times 2! = 240$
• Number of arrangements where Blue & Violet are adjacent:
  Treat (Blue, Violet) as 1 unit $\Rightarrow 5! \times 2! = 240$
• Number of arrangements where both pairs are adjacent:
  Treat both as single units $\Rightarrow 4! \times 2! \times 2! = 96$

3. Use the principle of inclusion-exclusion to find the number of ways where no indistinguishable colours are adjacent.

Using the complement method (Total $-$ ways at least one pair is adjacent):
$\text{Ways for 6 bands} = 720 - (240 + 240 - 96)$
$= 720 - 384 = 336$

(Alternatively, if relying on previous parts: $720 - [\text{Ways for 4 bands}] - [\text{Ways for 5 bands}] = 720 - 96 - 288 = 336$.)