Why did the gates clap shut and sent him flying backward?
Although he fed his ticket, he couldn't walk through.
What mistake did he make?

Why did it had snapped shut again, trapping him by his nose?

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At Underground Station.
He watched as the Browns fed their tickets into a slot in the barrier. However, being on the short side, he didn't see them take it out again from the slot on top. He posted his own ticket and was about to walk through when the gates clapped shut and sent him flying backward. A stern-looking ticket inspector opened the barrier and handed him back his ticket.
"Thank you, Officer", said Paddington.
He was so busy raising his hat that by the time he reached the barrier, it had snapped shut again, trapping him by his nose.
"Erb...? Excuse be, Obbicer?" he called.