The critical question is, how many full or nearly full oxygen cylinders did Mallory and Irvine have at their disposal on summit day? The absolute minimum appears to be seven: From Camp IV, Mallory carried one, Irvine two, the porters six; they wouldn't have needed first eight and then four porters if they had had fewer cylinders. They had used the better part of two on the way up, so seven were left. (Even if they had used one during the night, they still would have been left with six.)

When Odell arrived at Camp VI, he noted that there were oxygen cylinders inside the tiny tent but didn't say how many. There were at least two—the empties that Mallory and Irvine had used on their two-day ascent. The day before, Mallory had written to Odell that they'd probably push to the summit on two cylinders each, indicating that they had a choice of more. Also, none of the 1924 expedition members believed oxygen was of any value whatsoever on the descent, so there would have been no reason to leave spares behind in reserve.

In his note to John Noel, Mallory had told him to look for them "crossing the rock band under the pyramid or going up skyline at 8.0." Odell and others interpreted "crossing the rock band" as surmounting the Second Step, high on the Northeast Ridge. At 12:50 p.m., when Odell saw them doing what he thought was just that, he concluded that they were nearly five hours behind schedule.

In fact, nothing in the note suggests that Mallory intended to reach the Second Step by 8 a.m. What it does demonstrate is that he was still uncertain whether they would climb through the Yellow Band, as Norton and Somervell had done, or go directly up the ridge, his preferred route. In the end he chose the latter, and the two were "going up skyline" only 45 minutes to an hour later than estimated. We know this because of "No. 9," the spent 1924 oxygen bottle that Richards retrieved from the Northeast Ridge. Mallory's envelope notes show that No. 9 had 110 atmospheres of pressure. At a full flow rate of 2.2 liters per minute the bottle would have lasted three hours and 40 minutes. If we accept that Mallory and Irvine started near sunrise as Mallory had planned, oxygen cylinder No. 9 would have gotten him (or Irvine) some distance along the crest of the ridge before running out between 8:45 and 9:15.

Cylinder No. 9 also tells us that Mallory and Irvine were climbing strongly that morning. It was discovered 850 feet above Camp VI. Dividing that distance by the time the bottle lasted yields a perfectly respectable climbing rate of 230 feet per hour, roughly the same rate that the 1999 research expedition climbers took to cover the same distance. Moreover, Mallory and Irvine climbed before the era of fixing ropes and would have moved more quickly than modern-day mountaineers, though they would have spent somewhat more time sniffing out the best route.

Finally, cylinder No. 9 was found only 620 feet away from the base of the First Step. If Mallory or Irvine discarded No. 9 and switched to a fresh cylinder sometime between 8:45 and 9:15 a.m., they would certainly not have been at the First Step when Odell saw them at 12:50 p.m. Barring some lengthy, inexplicable delay, they would have been much higher. We can only conclude that Odell was right the first time: He saw Mallory and Irvine at the Second Step, or very possibly higher. Indeed, nothing in his topographical description fits any feature of the First Step.

Andy Politz, who made a point of climbing to the spot where Odell had stood 75 years earlier, remains convinced that what Odell described can only be interpreted as the Third Step. But if bottle No. 9 was discarded below the First Step, at about 9 a.m., it would have been extremely difficult for them to have made it as far as the Third Step by 12:50.

If the First Step is impossible and the Third Step seems unlikely, the only alternative is the Second Step. Its hundred-foot limestone band is climbed in three stages: a traverse to the right to a short rock climb, a steep scramble up a very small snow patch, and finally an ascent of the relatively short vertical headwall near the top. What Odell could have seen was the two climbers coming up that small snow patch and then scaling the headwall at the top "with alacrity."

The 1975 Chinese expedition installed a rickety aluminum ladder on the highly exposed vertical wall, and since then everyone summiting Everest from the north side has relied on the ladder to surmount the last pitch of the Second Step. Only one other team, a 1960 Chinese expedition, had summited without the benefit of a ladder. The 1999 Mallory and Irvine Research Expedition sent Anker, its best technical climber, to find out if Mallory could have, too.