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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

 Jul 13, 2020
edited by iamadumb6thgrader  Jul 13, 2020
 #1
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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   cheeky

 Jul 13, 2020
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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
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MAYBE go backwards from the LCM       LCM  4 5 6 = 60        I do not know if that always works !

ElectricPavlov  Jul 13, 2020
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In this case, it doesn't work. But, thanks EP for the ideas!

 

-iamadumb6thgrader

iamadumb6thgrader  Jul 13, 2020
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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
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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
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For sure !    LOL   

ElectricPavlov  Jul 13, 2020

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