I've been exploring discrete math and came across this apparently simple problem, but can't seem to solve it:
King Uxamhwiashurh had 4 sons, 10 of his male descendants had 3 sons each, 15 had 2 sons, and all others died childless. How many male descendants did King Uxamhwiashurh have?
I thought about simply multiplying these values, obtaining $15\cdot2+10\cdot30+4=64$, but I'm sure there's something wrong about this. I'd be really grateful if anyone had some hints for this problem.
Welcome to MSE!
Assuming you meant to write $3$ instead of $30$, it's pretty much as simple as that.
In graph theory terminology, consider that each set of descendants mentioned is a set of vertices with a certain degree. We have a connected graph with $11$ vertices of degree $4$ (the king and $10$ of his descendants), $15$ vertices of degree $3$, and some number of vertices $x$ with degree $1$. Because it's a tree, we know $V = E+1$, and the sum of the degrees must be $2E$. So:
$$V =E+1 = 11+15+x \implies E=25+x\\ 2E=(11)(4)+(15)(3)+x \implies 2E=89+x$$
Solving this, we get $x=39, E=64$, which means $V=65$. Subtracting the King's vertex gives $64$ descendants.