The New Sudoku Players' Forum

[Hajime]

15 boys have 7 days to train before a soccer tournament.
Each of the 7 days they have to warm up by running around the field.
The coach ordered that they run in 5 rows of 3 boys.
Now a boy stated that he wants each day 2 other boys in his row.
So after 7 days he will have all other 14 team members in his row.
Suddenly all other 14 boys want that same arrangement.
How must the coach arrange the 5 rows with 3 boys during 7 days?

[rjamil]

As per google AI overview:

The coach must use a design where 15 boys are split into 5 groups of 3 each day for 7 days so that every pair of boys is in the same row exactly once. This famous puzzle is known as Kirkman's Schoolgirl Problem.

R. Jamil

[Hajime]

Yeah, I tried to mask the schoolgirls with a soccer team, but AI is too smart.
Here an animated gif that demonstrates a solution:

The gif comes from https://math.stackexchange.com/questions/1202892/is-there-a-memorable-solution-to-kirkmans-school-girl-problem

[rjamil]

As per Wikipedia article, there are exactly seven solutions to this riddle, as originally listed by Frank Nelson Cole in Kirkman Parades in 1922.

R. Jamil