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There were over 280k online entries for the JP Post Stamp Box, not including the physical mail entries or boxes already sold at the annual stamp convention. 100k boxes are being produced (potentially more on the way but let's be real, that ain't happening).
It's insane to me that they thought to combine to heavily collectible markets, stamps and Pokemon cards, and not think the demand would outstrip supply. I'm not even sure how this will play out for the foreign market since you needed a domestic Japanese address and could only apply twice per resident.