# three "groups of musicians"

## What should replace the question mark? Explain why.

If,

   001 111 100
|   |   |   |
|   |   |   | = 2:3
|   |   |   |

010 111 100
|   |   |   |
|   |   |   | = 2:3
|   |   |   |

100 111 100
|   |   |   |
|   |   |   | = 2:3
|   |   |   |



Then,

   000 110 100
|   |   |   |
|   |   |   | = ?
|   |   |   |


The question mark should be replaced by:

13:15

Because a 'group of musicians' is a:

band, and so three groups of musicians are a triband, a word which is used in vexillology to mean a flag with three coloured stripes.

Now we realise that these line images must represent...

...triband flags, with their two key properties encoded:

1. The three colours are represented by the three binary triplets. The three 0/1 columns of each triplet represent the RGB colour model - column 1 represents red, column 2 is green, and column 3 is blue, with a '1' in a column indicating the presence of that colour, and a '0' its absence.

2. The ratio of the lengths of the two dimensions of the flag, height:width.

The three examples can be interpreted as...

the flags of France, Italy and Peru:

001 | 111 | 100 is blue, white, red (since 111, the presence of red, green and blue all together makes white) - the colours of the flag of France

010 | 111 | 100 is green, white, red - the colours of the flag of Italy

100 | 111 | 100 is red, white, red - the colours of the flag of Peru

So the final combination makes...

the flag of Belgium:

000 | 110 | 100 is black, yellow, red (since 000 - the absence of red, green and blue - makes black, and 110 - the presence of red and green together - makes yellow.

And the relative dimensions of the sides of the Belgian flag are 13:15, which is the answer we seek.

• Ahh, that's clever
– oAlt
Dec 26, 2022 at 11:57
• Correct. Well done! Dec 26, 2022 at 11:58