Bulk Archive in Gmail

I have just found a solution to a Gmail problem that I could not find by searching on-line

A close relation had 11,000 emails in her inbox and wanted to archive them to get them out of the way. Doing 50 at a time (which is apparently all that is allowed) was a waste of too much of her, or my, life.
Here’s what I found you do:
  • Come out of Inbox by choosing ‘All Mail’.
  • Tick the ‘Select All’ button, top left.
  • Look for the message which says ‘All 50 messages on this page are selected. Select all 52,479 messages in All Mail‘ (or however many you’ve got)
  • Click the underlined link in that message
  • Press the Archive tab (Yes – you seem to be archiving things that are already archived!)
  • Say Yes, (= I really do want to archive 52,479 messages)
  • Wait for a minute or so
  • Bingo!  Clean inbox.
This may be blindingly obvious to everybody else, but it foxed us for quite a long time. Perhaps it will help someone else.