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A fast-food chain sells chicken nuggets in boxes of 8, 9, and 20. What is the largest number of chicken nuggets that is impossible to buy?
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A fast-food chain sells chicken nuggets in boxes of 8, 9, and 20. What is the largest number of chicken nuggets that is impossible to buy?
THANK YOU AGAIN!
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Ignoring boxes of 20 to start, you can buy the following numbers: The first column is using boxes of 8, each succeeding column is substituting an increasing number of boxes of 9.
8, 9
16, 17, 18
24, 25, 26, 27
32, 33, 34, 35, 36
40, 41, 42, 43, 44, 45
48, 49, 50, 51, 52, 53, 54
56, 57, 58, 59, 60, 61, 62, 63
All values above 63 are buyable by adding one or more boxes of 8 to the final row.
The highest value is therefore 55.
But 20+35 = 55, so that is buyable.
47 is the next highest, but that is 20+27. Likewise for 46.
39 is the highest number that cannot be bought. Q.E.D.
8, 9
16, 17, 18
24, 25, 26, 27
32, 33, 34, 35, 36
40, 41, 42, 43, 44, 45
48, 49, 50, 51, 52, 53, 54
56, 57, 58, 59, 60, 61, 62, 63
All values above 63 are buyable by adding one or more boxes of 8 to the final row.
The highest value is therefore 55.
But 20+35 = 55, so that is buyable.
47 is the next highest, but that is 20+27. Likewise for 46.
39 is the highest number that cannot be bought. Q.E.D.
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The answer is infinity since you could keep buying quantities of either 8, 9, or 20 forever.
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I don't get you