Bob Ruyle

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@MatildaSpicer Euclid's Proposition 35 and Proposition 43.
(Propositions about parallelograms)

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@SilverBali7

[Bob Ruyle @bruyle1]

@SilverBali7

[Bob Ruyle @bruyle1]

@jamestanton @BradBMath The last table suggests a recurrence relation for f(N),
where f(N) = no. of ways of splitting N coins into three nonempty piles.

[Bob Ruyle @bruyle1]

@jamestanton Here's one possibility for an expression for the no. of ways to split N coins into three nonempty piles, (not counting order of piles).
No proof given here. But, the idea is based on same reasoning as given by @BradBMath in puzzle of a couple days ago.

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@BradBMath @jamestanton I think I followed your argument ... until the last bit where you calculated the value.
I get this:

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@eylemboss0306

[Bob Ruyle @bruyle1]

@asitnof @jamestanton Thank you!
I got the idea only after reading your contribution.

[Bob Ruyle @bruyle1]

@MatildaSpicer

[Bob Ruyle @bruyle1]

@MatildaSpicer Another way. Not necessarily a better way.

[Bob Ruyle @bruyle1]

@ai_meh_s @TaghiBehradfar S1 : S2 = 1 : 1