Two stamp collectors have completed a grown-up, multi-million dollar version of the playground swap, to finish an unparalleled compilation.
The coup by Bill Gross, a US financier known as the "Bond King", means he has the only complete set of US 19th Century stamps in existence.
He finally landed his "Holy Grail" - an 1868 one cent "Z Grill" stamp - after years of trying.
In return he gave up the unique stamps he recently bought for $2.97m (£1.67m).
He handed over the block of four "Inverted Jenny" stamps to Donald Sundman, president of the Mystic Stamp Company.
"It is truly the biggest event in the past 100 years. [The Z Grill] is like the Holy Grail of stampdom," said Charles Shreve, president of Shreves Philatelic Galleries, who represented Mr Gross at the swap.
Mr Gross needed the Z Grill to complete the first comprehensive set of US 19th Century stamps - something not even the US National Postal Museum has achieved.
There are only two Z Grills in existence. Mr Gross first tried to buy this example in 1998, but was outbid by Mr Sundman, who paid $935,000.
The blue Z Grill features Benjamin Franklin and is named after the experimental security grill on the back.
The swap implicitly gives it the same $3m value as the four Jennys - making it the most expensive single stamp ever.
The 1918 Inverted Jennys are so-called because they feature a Curtiss JN-4 biplane - known as a Jenny - mistakenly printed upside down.
This example of the rare stamps is unique because it has the printing block number - also upside down - in the bottom left corner.
Mr Gross paid the world record price for the Jennys only two weeks ago, specifically in order to offer the swap.
Mr Sundman, wearing a tie depicting the Inverted Jenny stamp, admitted to "a serious case of seller's remorse" after handing over his treasured item.
"I bought the Z Grill because it was the rarest stamp in the world. But I get a wonderful item in exchange," he said.
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