I hope that you enjoyed Saturday’s Mac Riddles, episode 198. Here are my solutions to them.
1: Visible vapour after I sync with Liverpool plus.
Click for a solution
iCloud
Visible vapour (cloud) after I (i-) sync with (what you hope to do with it) Liverpool (Apple internal name for CloudKit) plus (now iCloud+ as well).
2: Hanging decoration to fascinate an infant and myself brought a fiasco in the summer of 2008.
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MobileMe
Hanging decoration to fascinate an infant (a mobile) and myself (me) brought a fiasco in the summer of 2008 (launched on 9 July 2008 to replace .Mac, the successor to iTools, Steve Jobs was upset at its failure).
3: Within a week of the new millennium I came with a gun for online storage and more.
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iTools
Within a week of the new millennium (released on 5 January 2000) I came with a gun (known in slang as a tool) for online storage and more (it included iDisk, Mail, iCards and others).
The common factor
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They have all formed Apple’s online user services.
I look forward to your putting alternative cases.