Solving Seven - Numberphile

NUMBERPHILE

Videos by Brady Haran

[unvergebeneid]

I have a heuristic way of figuring out if a number is divisible by 7. The answer is always "no" and you're only wrong 14% of the time!

[dunsparceprez]

We need a Numberphile video on why James doesn’t age

[yuhboi]

Instructions unclear - drew symbol, now my brother's soul is trapped in a suit of armour

[MatthewGlenEvans]

"I thought I invented a thing, but I didn't invent a thing" such a bittersweet feeling

[tBagley]

you can also subtract multiples of 7 from your original number wherever you find them, and also change all 7s to 0s, 8s to 1s, and 9s to 2s if it helps. so for the number brady chose, I know that 3, 714, 289 will only be divisible by 7 if 3, 000, 002 is. so just start at 3, follow the arrows 6 times (taking you back to 3), and add 2 to get 5.

[wmpowell]

I actually derived this method myself while at a math competition. I knew I would be answering a question on modular arithmetic and could anticipate it being modulo 7. So before time started, I made a multiplication-by-3-modulo-7 table to aid me.
It wouldn't be too far of a stretch to call this method "the universal divisibility test" since it can be generalized to any base.

[marklonergan]

"you can do it in your head - multiply by 10, add the next digit, multiply by 10, add the next digit"

I mean, that essentially is how you do long division already. Find the remainder, append a further digit onto the end, that is just multiplying by 10 and adding it.

[CrashSable]

"So how do you see if a number (in base ten) is divisible by seven just by looking at it?"

"Well, you divide it by seven and see if there's a remainder..."

[adamplace]

Alright, the red arrows being the way to multiply by 10 and keep the remainders got me. That "ohhh!" moment keeps me coming back to this channel as much as anything. Well done!

[DaTux]

"I thought I'd invented something but turns out it already existed." - Nearly every 19th century mathematician after checking Euler's collected works.

[DanielTompkinsGuitar]

All the pinging sounds for the numbers around the circle animations make a C major scale, and since there are only seven numbers, we never get the 8th number bringing us back to C. So each illustration left us hanging—musically. I kept mentally singing the C note after each illustration to complete the octave 😂

[Hawksmoor]

Initially I thought "OK, we're counting mod7..." As James described how the process works I realized "Oh, this is just long division with a graphical assist!"

[AaronFBianchiJupiter]

The fact that Brady has been using the notes from C to B instead of D to C sounds like he used the B Locrian scale and it feels like a sneeze that never comes

[monstronamaguederaz]

Legend says this method was discovered by a man called Stephen Strange.

[wtfpwnzred]

I would rather carry remainders and divide by 7 in my head. This looks like so much extra work

[Markus_]

"I have it on my phone." - brilliant!

[RobinDSaunders]

As well as working for any divisor, this method also works for any base. But when the divisor is prime, there are close relationships with finite fields, and in particular discrete logarithms which have applications in cryptography.

Kudos to whoever thought of using a musical scale for the illustrations, presumably because it's another periodic pattern of seven objects. It's a neat touch!

[shinigamisteve]

Beautiful! I also like that you only have to show half of the clock, as the rest of the clock is symmetric. That is because for mod n, 10k is congruent to n - 10(n - k)

[jackmojo]

Snape: "Turn to page 394." Harry: "But that's not evenly divisible by 7..."

[amethystklintberg]

Oh my goodness, I discovered this circle picture too! (As a way to investigate the divisors of Mersenne composites.) I’m actually doing my master’s in number theory on it right now! 🎉 Finally, I have a corroborating video to point to, that shows this diagram is helpful to mathematicians! 🙏