A Maths Puzzle: Balls, Solution and The Chinese Remainder Theorem

[Gmoney2697]

show us your collection please

[Redarthas]

How do I get as many balls as you? Tell me your secret! xD

[carson032000]

can you help me to prove the chinese remainder theorem, i need to know about for my next cse midterm

[PantheraTigrisM]

b. sorry should read, since numbers whose digits whose digits add up to be a three multiple are divisible by three without remainder, numbers whose digits add to be three multiples must be skipped

[PantheraTigrisM]

ok my solution...

a. must be an odd number.

b. since #'s whose digits add to be a multip. of 3 , the digits cant add up to a 3 multi.

c. since all multi of 5 end in 5 or 0, and we must have remainder of 4, it must end in a 4 or a 9. cant be 4 that would conflict with a

then i just realized that if i had a number that when divided by 7 that followed a-c

but had a remainder other than 6 add a number that when divided by 7 had a remainder of 1 however many times to get a remainder of 6 and so on

[fabian696969]

I gave up on equations and mods so I started doing trial and error after finding the number ended in 9 and then added 110 for every trial. Sadly I gave up at around 1000 because I assumed no one owns more than 1000 juggling balls lol :p

[Renegade655]

i always love the questions that you throw out at youtube, always good ones to keep your mind wondering. keep this up singingbanana!!

[rockstarduh5]

At first I thought it was like some sort of super 5 by 5 matrix. haha I was wrong.

[sidchuownz]

Easy case of Chinese Remainder Theorem :/

[thejumperkin]

i did the same as dave597 haha, couldnt even understand how half of what you said worked though o.O

ill rewatch it a few times and figure it out eventually..

[Zarranious]

Hi singingbanana, Im 10 and love maths.I got it completly wrong though.I started of thinking you had no more than 60 balls, so I wrote my 2,3,5,7 &11 times tables up to 60.I then added 1 to all the two time table,2 to all the 3's, 4 to the 5's,6 to the 7's and to to the 11's. I looked at the twos and Knew it was odd.I crossed out the even numbers.Looking at the 5's I knew it would end in a 9 I saw 39 was in all the coloums except the 11's so I knew I would have to go further but I was to busy.

[singingbanana]

You did really well. You were nearly there.

[Ishyaboiyounghomie]

How exactly do you figure out the equation for the ?.

if you had x = 4 mod 7 and x = 5 mod 18

[singingbanana]

Since 7 and 18 are coprime the answer will be mod 126, (126 = 7*18). By inspection I can see the answer 95 satisfies both congruences (95 = 4 mod 7 and 95 = 5 mod 18). So the final answer is x = 95 mod 126.

[singingbanana]

Sorry removed your comment by accident. They really shouldn't put 'remove' and 'reply' next to each other.

There is a formula, I tried to explain it in the video. In this case, since 1 = (2 x 18) - (5 x 7) then 7 and 18 are coprime.

And the solution to x = 4 mod 7 and x = 5 mod 18 is

(4 x 2 x 18) - (5 x 5 x 7) = -31 = 95 mod 126

[askmagus]

2309! Wow, you were blessed with many balls...

Though it must be difficult to walk carry all those with you.

[jimmyluc]

lol..

[CogitoErgoCogitoSum]

Now, what I saw was that if you put your balls into piles of "n", you will have precisely "n - 1" left over. This is true regardless of n. I also noted that your n was each prime number from 2 to 11. I didnt use modular arithmetic. I simply multiplied the prime numbers 2 through 11 together and subtracted 1. Seems simpler to do it that way, though likely not a general solution technique.

[CogitoErgoCogitoSum]

"All the way down"... like turtles? I just thought that line was funny, given the context

[VIBRAXBOY]

this is actually one of those videos as you feel like a retard after watching;) jesus crist that was way to much

[Fearless1124]

Um...??? The Chinese Thereom just confused me... I think I got smarter??!!

[MysticalGohanZ]

damn i got 2099 balls...it was soooo close...

[singingbanana]

Nice work though, I am reading your comments :)

[MysticalGohanZ]

thnx...k i`ll tell u how i tried to solve..becoz i had no idea of chinese theorem, i tried the trial n error method....u said for piles of 11, 10 balls remain...so i tuk all multiples of 11 n simply added 10 to them so naturally the remainder will b 10...now for piles of 2, 1 ball remains which means the final answer is an odd number..so i rejected all even multiples of 11 n multiples which end in 5 coz they r completely divisible by 5...then i got 2099 as anwer..small calculation mistake may b

[singingbanana]

Your method was fine. Don't worry about the Theorem, just thought I'd show people something new.

[zyzzyzus]

I thought you had 170945114945190252226559 balls

[MKProductions23]

Can I marry your brain.

[rotnakleugim]

doesn't that box say this way up, and you put it wrrong

[DKDABU]

Nice Explonation why it was like that mate.. Learned something new.. I think.. :D

[singingbanana]

Thanks, because I get the impression this explanation wasn't quite as clear as I had intended.

[kyle7447]

wow this is so awesome!

[MaskedYoYoGuy]

there was not 2000 balls stacked up on the box i thot there was 21

[LunarFuror]

if there were 21 then there would be none left over from 7

[Swopedo]

i hate math. maybe i cann learn someting from you ;)

[swimmersrsick1]

confusion, "i have a lot of balls" funny quote

[seansean35]

YHUSSSS I WAS RITE AFTER 3 whole HRS!!!

[vs5799]

CONGRATZ!!!

[TyYann]

Yes, I fancy an ice cream.

Thank you for this video!

[ghfreakwierdo123]

the second one made a lot more sense

[grande1899]

At least I was right. It did end in 9 =p

[ahvaleshoma]

explosionnnnnnnnnnn!!!!!!!!!!1

in my head

[MaffiasAngelO88]

Usually I follow math really well, numbers don't scare me, but I think I'm begining to develop a new phobia lol!

Think I'll watch it again in a couple of weeks, when the pups old enough to feed its self, and I get more than 78 minutes sleep a night: D

[AutosuggestionJD]

Subterranean Homesick Singingbanana?

[peterabottt]

yes, he has a lot of balls

[SousukePanic]

after watching the vid twice i think i finally get it...barely lol

[percast]

hmm, I'm kinda confused, gonna watch it again

[JesseMercArt]

0:45 God I hope he knows what that implies. . .

[ChattyBug]

I think i have a migraine coming on...I re watched until I basically understood it, but I am only 12 and, whoa, it uses brain power!

[602rafizzle]

my brain exploded.

[emjay1264jr]

i was close i got 66 i just had 2243 balls missing lol

[rootbeer9000]

wow i was way off i never even could come close to an answer

[blizzmonkin]

that guy is amazing

[FlySpades11]

sort of confusing

[singingbanana]

Sorry friend, I wanted to use the problem as an excuse to show people something new - the Chinese Remainder Theorem. Whatever you take away from this video is cool.

[robgrime1]

does that include the balls you've got in you room here?

[PazicianMagic]

My guess was 2310! I missed the last part :D

[Marboi808]

haha he has alot of balls

[TH3GHOST2]

I don't know what the hell you just said but well done

[JellyfishPie00]

huh?

[SvAbO666]

ahhh... now i get it.

just kidding dude, i have no idea what u have been talking about XD but i watched it till the end :P

[omaristheman]

kewl puzzle