There can be 4 boys or more between any two girls.

For the maximum number of girls, we keep the number of boys to as small as possible.

So, we only consider 4 boys between two girls.

GBBBB (5 people, first row)
GBBBB
GBBBB
GBBBB...

...GBBBB
GBBBB
G

There must have been 14 full “rows” based on the above plus one extra “G”.

There must have been 14 G + 1 G = 15 G.

It's better to arrange in a single line as they don't queue in rows.

Min 4 boys between 2 girls means :

GBBBBGBBBBGBBBG.... GBBBBG

This means we just put exactly 4 boys between every 2 girls so we can have the maximum number of girls and minimum boys possible for a total of 71 people.


Now, notice that the pattern GBBBB is repeating.

So group the first four boys and 1st girl as 1 set. Do the same for the next 4 boys and 2nd girl.

In each set there are 5 people.

Now when you reach the last set, a girl has to be present to flank the last boy.

So if we remove her from the total, we will know how many sets there are.

71 - 1 = 70

Number of sets = 70 ÷ 5 = 14

So there are 14 girls in the sets altogether.

Add back the last girl we removed earlier on,

Total = 14 + 1 = 15

Why divide by 5 and not 6

Because the pattern GBBBB repeats, not the pattern GBBBBG.

The queue isn't

GBBBBG GBBBBG GBBBBG




If you divide by 6, you are trying to find how many GBBBBG there are. But this cannot work as the queue is


GBBBBGBBBBGBBBBG....

The girls in between are flanking boys on each side

Thank you for your time and effort

Welcome

I initially planned to write in a single row, but soon realised that the reader would not be able to do counting.

Hence, I placed them in equivalent rows of 5 to denote that the sixth girl and the seventh to tenth boy are actually continuous had they been placed in a single row.

It’s the same reason why tally charts are not labelled as IIIIIIIIIII..., but instead as IIII with a strike in the middle.

What ?!

Follow J’s single row arrangement.

I only reclassified the single row into multiple rows of 5 for easier visualisation.

J can you have me with another question

Oh ok I understand

Students will still have to train/hone their abilities to count groups from a continuous line, i.e mental visualisation.


Given such a line , the faster way is to draw vertical lines between groups/units , much like in model drawing

Eg. GBBBB|GBBBB|GBBBB|GBBBB|G

Sure Manoj

J did you see the question

Yes, give me a while to type it out