This is a two-novella book in the Revelation Space universe.
"Turquoise Days" is set on a Pattern Juggler planet where the humans are trying experiments to find out just what Pattern Jugglers are, when other humans arrive who have differing ideas about how to treat the aliens. This happens some time before Absolution Gap chronologically.
"Diamond Dogs" has a group of humans from Yellowstone (this edges between The Prefect and Chasm City chronologically) head out to foil a large spire on an empty planet. The spire requires them to figure out mathematical problems that increase in difficulty as you go up the apire. If you get one wrong, the spire tries to kill you.
