Which of the following is a stiff noseband on a halter or bridle and is sometimes used with long strap in training?

The cavesson is a type of stiff noseband often used in conjunction with a halter or bridle. Its primary function is to provide control over the horse's head while allowing for the use of different training aids. The stiffness of the cavesson helps maintain the position of the noseband, ensuring that it doesn't shift or move excessively, which could lead to discomfort or confusion for the horse.

Additionally, the cavesson can be used with a long strap, known as a longeing strap, which facilitates various training exercises, including lunging. This setup allows the handler to give clear cues without interference from the horse's mouth, promoting effective communication during training sessions.

In contrast, options such as the gag and the flash serve different purposes; the gag is a bit that applies pressure to the horse's mouth and poll, while the flash is a type of noseband designed to keep the horse's mouth closed or to prevent the horse from evading the bit. The term 'blinch' does not typically refer to any standardized equipment used in horse riding or training, thus making it less relevant in this context.