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- Jan 26, 2012

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- Thread starter
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- #1

- Jan 26, 2012

- 4,058

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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- Jan 26, 2012

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1) Sudharaka

Solution (from Sudharaka):

This problem stems from the Frobenius Coin Problem. Since there's no explicit formula known to calculate the Frobenius number when the number of elements of a set is three or more, one way to solve this problem is to a numerical method such as the Rödseth's algorithm.

Some additional comments:

Here's how you can make the numbers 44-49 with 6, 9, and 20.

$$44 = 6 + 9 + 9 + 20$$

$$45 = 9 + 9 + 9 + 9 + 9$$

$$46 = 6 + 20 + 20$$

$$47 = 9 + 9 + 9 + 20$$

$$48 = 6 + 6 + 9 + 9 + 9 + 9$$

$$49 = 9 + 20 + 20$$

You can continue the sequence by adding 6 to the above list so again we see that 43 is the largest number we can't make this way.

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