Question: Find the smallest number that has a remainder of 3 when divided by 4, a remainder of 4 when divided by 5, and a remainder of 5 when divided by 6.

I used the chicken nugget theorem and got 59.

(you list them out starting from 7, 9, and 11 unitl you get a common number)

Besides guess and check, what other ways are there?

-iamadumb6thgrader

iamadumb6thgrader Jul 13, 2020

#1**+2 **

That is the method I used the othe day while solving one of these....it might be a little shorter to arrive at the number if you start with the largest divisor in the question: '6 ' with remainder 5

11 23 29 35 41 47 53 59

I do not know an eaiser (or another) way to solve these.....maybe something with the modulo function (of which I am not very familiar)....

Let me know if you find the true 'mathematical way' ! ~ EP

ElectricPavlov Jul 13, 2020

#2**+1 **

Hello, EP. I understand the way you told me, and that is SUPER helpful. Now I can do the problems a bit faster. You are amazing at math unlike me!

-iamadumb6thgrader

iamadumb6thgrader
Jul 13, 2020

#3**+1 **

MAYBE go backwards from the LCM LCM 4 5 6 = 60 I do not know if that always works !

ElectricPavlov
Jul 13, 2020

#4**+1 **

In this case, it doesn't work. But, thanks EP for the ideas!

-iamadumb6thgrader

iamadumb6thgrader
Jul 13, 2020

#5**0 **

No...I mean START with the LCM 60 and count__ backwards__ ....first one with a 5 remainder when divided by 6 is 59

ElectricPavlov
Jul 13, 2020

#6**0 **

Oh, that makes sense. I asked one of my friends about it, and he said it was called the "chinese theorem".

iamadumb6thgrader
Jul 13, 2020