Offsides is when a player crosses the blue line before another player on the same team with the puck crosses into there zone. The player with the puck must enter there zone first. This is to prevent a player from just sitting by the goal waiting for someone to pass the puck to them so they can score.
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No player is allowed to enter the attacking zone ahead of the puck. If they do, they are offside and play is stopped and there is a face-off in the neutral zone. If the puck leaves the attacking (offensive) zone all players on the attacking team need to "touch up" by going back to the neutral zone before bringing the puck back in. If the puck is brought in offside but controlled by the defending team it results in a delayed offside. The offside will then only be called if an attacking player touches the puck. If the defending team brings the puck back out of their zone the offside is negated and they are allowed to continue playing the puck.