I was watching the Mahabharata and they spoke about the 3 kinds of debts that one has to fulfill in his/her lifetime: God’s debt, Sage’s debt, Ancestral debt.
All must fulfill their debts three,
God’s, Sage’s, Ancestral surely,
Before death and leaving body,
Else life itself is insulted sadly.
These debts not ordinary do be,
God’s debt – Lord Vishnu’s be,
Sage’s debt – Lord Shiv’s be,
Ancestral debt – Brahma’s be.
God’s debt by charity fulfilled be,
Sage’s by acquiring, giving be,
But of the knowledge definitely,
Ancestral debt by having progeny.
God’s debt can be fulfilled by doing charity work. I am not surprised by that. It is known in many esoteric circles that charity is a very important deed. The Bible and Masonic literature talk a lot about charity.
And it goes without saying that ancestral debt can be fulfilled by procreating and continuing our ancestral lineage. That is not to say that one should procreate mindlessly but instead procreate with high morality and spiritual standards. One has to bring children to the world so they help improve the world and not “pollute” the world and be like parasites.
Two things do not remain for ever in humans: youth and strength
Two things beneficial for every human: good manners and generosity
Two things that hurt every man: darkness and corruption
Two things every man hates: envy and bitterness
Two things pursued by every man: fame and money
Two things that never change in a human: looks and character
Two things you spend your life between: evening and day, tiredness and restfulness
Two things that conflict your soul: the lust of the body and the lust of the soul
Two things are enemies of health: deep sorrow and deep love
Two things are enemies of peace: greed and envy
Two things are enemies of the society: the traitor and the lazy
Two small things: the heart and the tongue
Two stones: gold and silver
Two alternates: day and night
Two whites: water and yogurt
Two courts: the world and the afterlife
A brother said to his sister: “I have as many sisters as brothers”
His sister replied: “I have twice as many brothers as I have sisters”
How many brothers and sisters exist in this family?
I figured that it’s a nice exercise for the Z3 theorem prover. All I had to do is express the riddle in a series of constraints and ask Z3 to try to find a solution.
The following is a Z3Py program that expresses the riddle:
# Create a solver instance
s = z3.Solver()
# Create two variables representing the total number of males and females (m and f)
m, f = z3.Ints('m f')
# The brother said: I have as many brothers as sisters
s.add(m - 1 == f)
# The sister said: I have twice as much brothers as I have sisters
s.add(2 * (f - 1) == m)
# Check for the solution
if s.check() == z3.sat:
sol = s.model()
print "Brothers: %d, Sisters: %d" % (sol[m].as_long(), sol[f].as_long())
When we run the solver, we get the following solution: 4 males, 3 females.
If you prefer the good old systems of equations, we can solve it like this:
The brother said:
m - 1 = f (1)
The sister said:
2 * (f - 1) = m (2)
So we have 2 equations, let's do some substitution:
-> f = m - 1 (1)
-> 2f - 2 = m (2)
--> m = 2f - 2 (2)
--> f = 2f - 2 - 1 (1)
--> f = 2f - 3
--> f - 2f = -3
--> -f = -3
--> f = 3
--> m = 2f - 2
--> m = 2*3 - 2
--> m = 6 - 2
--> m = 4