According to Shakuntala Devi, there is no quick test to see if a number is divisible by 7
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Books:
Figuring (The Joy of Numbers) and All in a Wonderland of Numbers by Shakuntala Devi
Mathemagic by Royal Vale Heath
Mathematics Magic and Mystery by Martin Gardner
Self-Working Number Magic by Karl Fulves
The Trachtenberg Speed System of Basic Mathematics
It Figures by Clive Dickinson
The Fascination of Numbers
The Guiness Book of Numbers
Calculator Fun and Games
Adam Spencers Book Of Numbers