At this point, you might ask, "why bother limiting the palette? What do I stand to gain?" The answer is Harmony! Mood!. When all the strokes and washes in a painting are made from the same few components, the result has an overall cohesiveness that is difficult to achieve by other means.
Choose three colors, one red, one yellow and one blue, and use only those three to make a version of the image you brought home, or of one below. You can plan your choices with an eye toward the most accurate interpretation possible, or you can go with your gut feeling about how your components fit together. Some scenes benefit from a palette that keeps the key low, others welcome a noisier selection.
The "limits" that a limited palette impose on your painting may tempt you to stretch the array of colors just a little. As we saw, ultramarine and burnt sienna can't make a true purple. There's too much yellow in the burnt sienna, which turns the mixture brown. But if you break out and add a little violet to your painting, it will look out of place in the world that's otherwise all made from only three colors. Let the purple be kind of brown, at least for this exercise, to find out what you can really do within the limits.