How primary colors combine to create secondary colors depends on whether you're combining different colors of light, or combining different colors of paint or ink. The former is called color mixing by addition while the latter is called color mixing by subtraction. Here's the difference:
When you combine different colors of light, the light that reaches your eye is actually the sum of the individual colors. On the other hand, when inkjet ink is squirted onto a page, the color you observe depends on what light is absorbed by the ink. If you combine inks, this increases the amount of light absorbed, and so it decreases the light that reaches your eye. Hence, subtraction.
For combining light, the primary colors are usually considered to be red, blue, and green. Red+blue = magenta, red+green = yellow, and blue+green = cyan. Computer monitors work by mixing different colors of light. If you open something like PowerPoint or Word and make a big colored circle, and attempt to change its color, you can find an option buried deep somewhere to specify the amounts of red, blue, and green in the color of your circle.
Now for inks. For your three primary inks, you want one that absorbs red, one that absorbs green, and one that absorbs blue. The one that absorbs red reflects blue and green, and so the color we observe is cyan. The one that absorbs green reflects blue and red, and so we observe magenta, and the one that absorbs blue reflects green and red, and so we observe yellow. Hence the three primary colors of ink are cyan, magenta, and yellow.
When we combine cyan and magenta ink, the cyan ink absorbs red, the magenta ink absorbs green, and so the resulting combination absorbs both red and green. As a result, what gets reflected is blue. Hence in inks, cyan+magenta = blue. By the same logic, cyan+yellow = green and yellow+magenta = red.
This is, of course, an oversimplification, but the basic idea is there.
(I teach a course in Light and Color. This is cool stuff.)
Hope that was clear. I've had a couple of beers. :-)
(Good luck with the puzzle.)
"It's only Neutron. We call him that because he's so positive." --from This Island Earth