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Scott Cram
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Numberphile recently did a video about divisibility tests:

On their second channel, they posted an excerpt not included in the above video, which contains what they believe may be the worse card trick ever:

Those of you who have the Ibidem books (or the original issues!) can look at the April 1956 issue of Ibidem and find this trick taught as L. Vosburgh Lyons‘ “Mentrick”. In that source, the method is taught more coherently than in the above video, and you’ll realize that the trick is performed better without cards, using a written grid (if only they employed some sort of writing surface in Numberphile videos!).

They do gloss over an important detail, however: that of finding how far away the starting number is from a multiple of 7. When making sure the original number isn’t divisible by 7, you can use the decimal amount to see exactly what the remainder would be. If you’re not already familiar with the fractions for sevenths, they follow easy patterns, as described in these articles:

As noted in the former article, you can just look at the first 2 digits, and quickly determine the needed remainder by dividing roughly by 14. For example, if the first 2 digits after the decimal point are 42, you can divide that by 14 to get 3, and that tells you that the number is 3 more than a multiple of 7. Did the original number when divided by 7 end in .71428...etc.? Then you can mentally divide 71 by 14 and know that the number is 5 more than a multiple of 7.
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