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

Solution to A Maths Puzzle: Balls, followed by an explanation of the maths behind it.

Original video here http://www.youtube.com/watch?v=QmLzX3xn8RE

Check out dave597's channel here http://www.youtube.com/user/dave597 and his solution here http://daveman.wordpress.com/2009/07/24/another-solution-to-a-maths-puzzle-ba...

Category:

Education

Tags:

• maths
• math
• mathematics
• problem
• puzzle
• solution
• number
• theory
• chinese
• remainder
• theorem

[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

[peterabottt]

yes, he has a lot of balls

[MKProductions23]

Can I marry your brain.

[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 :/