## Wednesday, February 06, 2013

### Hidden Equations

 AlgebraPart Three
So far we have looked at simultaneous equations that were hidden in plain sight, as it were.

Of course most puzzles that rely on equations try and hide the method behind flavour; either in the guise of an elaborate story, where a key piece of information is implied but not stated. Or as a diagram, hiding the maths behind abstract imagery.

Today I have a couple of new puzzles for you to tackle which use simultaneous equations in different ways. They should be familiar to you as some of the most common puzzles to appear in general puzzle books.

Picture Grid

Below is a grid of differently coloured shapes, each shape or indeed colour stands for a specific number and, when the four numbers in any row or column as added together, they give the result at the end of the column or row.

Can you work out the number that each shape represents,?

That shouldn't prove too challenging for you seasoned puzzlers, as long as you follow the logical path and find the right equations it should be simple.

Alien Invasion

Yet again the apocalypse has been predicted, only this time the seers of doom and destruction were right! Aliens have invaded Earth, the humans have been overthrown and it looks like the end is near, unfortunately the Government has no idea just how many aliens have arrived.

This is due to the Governments lack of aptitude and the aliens cunning ability to camouflage themselves. These aliens use cloaking technology to remain invisible, however, due to the lower levels of gravity on Earth as compared to their homeland, their feet and heads project outside of their cloaking field.

Scientists have ascertained that one kind of alien, the Xeomorph have one head and two legs each but the other invading species, the Yaksgar have four legs despite only having the one head.

Our troops on the ground have identified 39 heads and 106 legs. How many aliens of each kind have invaded?

Again, this is another common type of puzzle, heads and legs, and often includes other body parts too. Thanks to my good friend Owain for the alien species names. The Xeomorph and the Yaksgar will be back with us for future puzzles. Remember, find out what the equations are and then just work methodically.

Happy Puzzling