All of them arrived in New Zealand about five months ago. They had been working in Napier and Hastings before setting off on the holiday leg of their trip.
After hiking in Abel Tasman National Park, they arrived at Aoraki-Mt Cook National Park on Tuesday.
They decided to attempt the Ball Pass Crossing - a demanding two- to three-day alpine route - which crosses the Mt Cook Range between the Hooker and Tasman valleys.
Although well-prepared, and having left details of their trip in the intentions book, they soon got lost.
"It was quite hard to find signs on the Ball Pass ... We went much too far down into the valley," Alan said.
"We tried to cross over the mountains to get back on the Ball Pass. But there were huge gaps, like small valleys, so we had to climb a lot.
"Climbing got more and more difficult and we had no climbing gear with us."
They called 111 about 10.30pm.
"To go on would have been far too dangerous," Alan said.
Senior Constable Brent Swanson of Tekapo said they did the right thing. "They stayed put. If they'd tried to move ... they probably would have ended up in a place they wouldn't want to end up."
An immediate rescue was not deemed necessary on Thursday night because of the mild weather and the fact they were not in any immediate danger.
But there was no place to pitch their tent.
"It was quite cold and windy and we only had our sleeping bags but it was all right," Alan said.
"We had reception on our mobile phones so we knew that we could call the emergency number if we ever needed help."
At 8am yesterday, three Department of Conservation alpine rescue team members were taken to the scene by a Helicopter Lines chopper.
The hikers were short-roped to a location nearby where they could be hover-loaded into the helicopter, which returned them to Aoraki-Mt Cook Emergency Centre about 9.30am.
The three men praised the "friendly and helpful" rescuers.
"It was a great feeling to be rescued," Alan said. "It was an amazing feeling to know that now we can get home without any other trouble. It was a crazy situation to be in."
The men did not require any medical assistance and yesterday headed for Queenstown, where they planned to buy a personal locator beacon before their next hike, in Fiordland.