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He was descending the Matterhorn during a climbing trip in the Swiss Alps when a friend mentioned the forthcoming British expedition to Everest.
The 27-year-old statistician decided to apply when he returned to England.
I heard nothing about my application for some weeks, but then got a rather exciting phone call to come and meet John Hunt at the Royal Geographical Society.
It was a bit of luck - I was at the right age at the right time and people like Joe Brown, Don Whillans and Chris Bonington were much too young.
A few years later I wouldn't have had a hope of joining it.
I'd been a humble lieutenant in the Indian army, so the thought of meeting a full colonel was a little bit daunting in those days.
But that feeling didn't last more than 10 seconds. When one met him he was instantly welcoming and friendly.
At the end of that interview I thought that if I was to be refused a place on that expedition, I'd rather take that refusal from John Hunt than from most people.
About 10 days later I was in North Wales with climbing friends at the Pen-y-Gwryd hotel in Snowdonia.
I heard that there were still two places to be filled and four people still in the running, and I also heard I was one of the four.
So there was a nail-biting time for the next 10 days before I got the very exciting letter saying I'd been chosen.
But that arrived the same day as the names of the team were published in the papers.
When I went for my usual morning coffee with the other scientists I got a cheer when I went into the room.
All my colleagues were very pleased - whether my boss was pleased or not I don't know, but since he was a climber I think he was.
I was one of the first four people to go to the icefall and help prepare that way for the porters using ropes and bits of ladder.
Later on in the expedition I went up to Camp 5 and approached Camp 6, but then got horribly sick with the altitude and other things, so I had to go down.
I spent the rest of the expedition keeping the icefall open, while most of the others were up above it.
The most memorable moment was when Ed Hilary and Tenzing came down from the top. They were only 100 yards [91.4 m] away from the camp when we realised they'd done it - that was a superb moment.
We were all tremendously enthusiastic and rushed forward to shake them by the hand and so on.
That will always stick in my mind.
Then we suddenly realised we could possibly get the news back in time for the Coronation.
So at about 1600 James Morris [the Times correspondent with the expedition] and I started down the icefall - not the most sensible thing I've done from a mountaineering point of view.
By the time we got to the bottom we were very tired indeed and it was getting dark.
James said to me, "Take the rope off, Mike, I'll follow a little later." I refused - I dragged him on. We both collapsed into our sleeping bags and that was all till the next morning.
It was a great surprise to be met some way out of Kathmandu by a whole tribe of people.
There was a nasty political business in Kathmandu itself - there were cartoons all over the city showing an exhausted Ed Hilary being dragged to the top by Tenzing.
But generally speaking our welcome was very friendly indeed, and even more so in Delhi where Pandit Nehru was our host.
I think every member of the team would have liked to have been to the top - I certainly would.
But we did look upon it very much as a team effort, and the fact that those two got to the top was extremely satisfying.
Mike Westmacott climbed actively until a hip replacement operation in 2003.
He was president of the Alpine Club between 1993 and 1995 and now lives in Cumbria with his wife, Sally.
Chaotic and often dangerous area of glacier.
A col, or pass, is a lower gap in the crest of a mountain ridge. The "normal" route up Everest goes via the South Col.
Welsh word for a glacially-scoured bowl in a mountain's side. Also called a corrie (Scottish) or cirque (French).
Reaching the summit of a mountain.
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