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They are probably measuring from the base, not height above sea level. Everest peak is about 15K ft above it's base, which is about 14K above sea level; Mauna Kea is about 13K ft above sea level, but its base is more than 25K feet /below/ sea level. About 40K overall for Mauna Kea vs 29K for Everest.
Thanks for your feedback. We will check and fix the issue.
Also got the cigar part right too!