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# A fast food chain sells chicken nuggets in boxes of 9,13, and 20. What is the largest number of nuggets that is impossible to buy?

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A fast food chain sells chicken nuggets in boxes of 9,13, and 20. What is the largest number of nuggets that is impossible to buy?

Guest Apr 10, 2015

#6
+92254
+5

Thanks Alan

6,9,20

Q=6a+9b+20c

(6a+9b+20c)modulo 6 = r

(9b+20c) modulo 6 =r

What numbers are possible if r=1

1x 7x 13x 19x 25x 31x 37x 43x 49=2*20+1*9     43 is the biggest that can not be packaged

What numbers are possible if r=2

2x 8x 14x 20=20*1       14 is the biggest but it is smaller than 43

What numbers are possible if r=3

3x 9=1*9                         3 is the biggest but it is smaller than 43

What numbers are possible if r=4

4x 10x 16x 22x 28x 34x 40=2*20        34 is the biggest but it is smaller than 43

What numbers are possible if r=5

5x 11x 17x 23x 29=1*20+1*9             23 is the biggest but it is smaller than 43

so

43 is the biggest number that can not be packaged!

That is so snazzy

Melody  Apr 12, 2015
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#1
+92254
+5

Mmm

you could buy any number N that satisfied this equation

N=9A+13B+20C         where A,B,and C  were all integers >=0

I would have thought that there was no maximum amount that could not be bought but I really have NO idea how to do this.

Maybe another mathematician can show us how?

I tried to enter it in wolfram|Alpha but I do not know how to do the input.

Melody  Apr 11, 2015
#2
+26642
+5

.

Alan  Apr 11, 2015
#3
+92254
+5

Your answer is great Alan.  It's going straight to the Pool Room !!!

If you do not understand this GREAT compliment it is because you are not Australian.

It comes from an iconic Australian movie made in 1997 called "The Castle"

The movie is hilarious and also very sweet.  Here is an extract.

The saying has even made it into the Urban Dictionary

http://www.urbandictionary.com/define.php?term=Pool+Room

NOW this is the second time I have written all this.

I actually went to great lengths to further explain what Alan had done.

THEN I lost the whole lot :(

Anyway if anyone wants more explanation, you will have to aske for it.  Sorry :(

Anyway Alan is a genious and this answer is fabulous!

Melody  Apr 11, 2015
#4
+92254
0

I just put this thread in our reference material thread.  I don't want it to get lost.

Alan, can you make up another one so that I can try it on my own?  :/

Melody  Apr 11, 2015
#5
+26642
+5

Melody, try it with boxes of size 6, 9 and 20.

.

Alan  Apr 11, 2015
#6
+92254
+5

Thanks Alan

6,9,20

Q=6a+9b+20c

(6a+9b+20c)modulo 6 = r

(9b+20c) modulo 6 =r

What numbers are possible if r=1

1x 7x 13x 19x 25x 31x 37x 43x 49=2*20+1*9     43 is the biggest that can not be packaged

What numbers are possible if r=2

2x 8x 14x 20=20*1       14 is the biggest but it is smaller than 43

What numbers are possible if r=3

3x 9=1*9                         3 is the biggest but it is smaller than 43

What numbers are possible if r=4

4x 10x 16x 22x 28x 34x 40=2*20        34 is the biggest but it is smaller than 43

What numbers are possible if r=5

5x 11x 17x 23x 29=1*20+1*9             23 is the biggest but it is smaller than 43

so

43 is the biggest number that can not be packaged!

That is so snazzy

Melody  Apr 12, 2015

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