Some users find out that it is possible to reach a contradiction in some levels. In particular in DragonBox Algebra 12+, one can end up with 4 = 5 in Chapter 10 Level 7.
Here's the explanation given by Jean, creator of DragonBox, and math teacher too : )
"On purpose we have designed levels where you happen to come to a contradiction if you perform an operation that is actually illegal when solving equations.
Our purpose with the game is to:
- teach algebraic rules and manipulation
- make players to actively think of strategies as how to solve the different puzzles
- discover properties of equations
4=5 is I guess achievable because you [...] you divided by "0". this can not be done for obvious reasons... We want the player to discover it and ask questions instead of being told not to do it."