You may remember that for one of my recent puzzles, “Damn right it’s MS Paint”, I posted this solution. One obvious issue with this solution is that it required guesswork to work out the numbers on the bottom row – until now, that is!

In his comment to the post, Xbalanque laid out a much better method of finding the bottom row numbers using some surprisingly simple algebra. I’ve quoted his method after the break along with a diagram to clarify matters (more MS Paint, appropriately enough), so please do check it out! I’ve also edited the original solution with a link to this post.

Here we go:

So, let’s start with what we know, to get those two numbers below the 30.

y+z=30
2+x=z
14+x=y
y+46=w
w+30=v

v is what we really care about, the ?

This gives us 5 equations and 5 unknowns. If we wanted to be really fancy, we’d just turn this whole thing (as in, the whole puzzle) into one big matrix thingy, and have a calculator or computer autosolve it, but let’s just do this by hand.

v=y+46+30=y+76
y+2+x=30
14+x=y

So…
14+x+2+x=2x+16=30
2x=14
x=7
y=21
v=21+76=97

So, without *any* guess work, we can find what’s in that ?

Well done to Xbalanque again for figuring this one out and posting it!

Vel.