Are the sums always right?

Yes. Every sum is made and worked out by the studio's own code, never by an AI, and checked before it prints: a space's sum always equals its color's answer in the key. Different spaces of the same color show different sums with the same answer (for example 4 × 9 and 9 × 4 for 36). Take-aways never go below zero and divisions always have whole answers.