This is problem 2, grades 11 and 12 for 2025. All right, a student threw five stones one after the other which hit a window at the points A, B, C, D, and E. When each stone hit the glass it created one or more linear cracks that stopped either at a previous crack or at the edge of the window. In which order did he throw the stones? We have A, D, A, C, B, E, selection B, A, B, C, D, E, selection C, B, D, A, C, E, selection D, B, C, D, A, E, and selection E, D, C, A, B, E. I apologize for the lots of letters there. Okay, so what I would recommend first doing is because all of the work here will be done sort of on the image, so let's really zoom into the image and let's remember the rules. So like one, they have to be linear and all of these are lines, so that's satisfied. But two, they stop at either walls, so they stop at like walls, or they stop at other cracks. So let's like sort of logic this out. If I have a point at which my rock hits the window and it stops at another crack, well that means that crack had to be there in the first place. For example, B, we know that it has to come after A because, or it comes after C, which comes after A, because it hits one of C's cracks. Okay, so then from there, let's uh, let's work this out. If something doesn't hit any of the other like points cracks, then we know it came first. So A hits D's crack, C hits A's crack, B hits C's crack, and E hits C's crack. So we know that D hits none of the other cracks, and thus it has to be first. So the first one is necessarily D. Then from there, well let's check who hits who again. So A hits only D, and each of the rest are reliant on either A or something that comes after A. So the second would actually be A. And we can like continue our thought process of only sort of investigating the cracks that have already been made. So like these cracks have already been made, so we should really only care about them on the board right now, and sort of consider them the new walls. Of course this would imply that C is next, so C is next. Drawing in those cracks, we can see that B is next because E is reliant on B. So B is next. And then finally E. And I won't drop that in because I would just be replicating the picture. But we're left with a final answer choice of D, A, C, B, E, which corresponds to answer choice A. That was a nice little puzzle.

stone throwing

crack sequence

window cracks

interaction analysis

order determination